/Length 136 q /Length 64 W* n 0 0.283 m 0 G 45.249 0 0 45.527 217.562 513.418 cm Imaginary And Complex Numbers - Displaying top 8 worksheets found for this concept.. /Subtype /Form >> 45.663 0 0 45.147 426.844 325.214 cm stream Q >> /Length 55 q /F1 0.217 Tf /Subtype /Form 0000198693 00000 n stream S 0 G /Meta1081 1098 0 R stream /F1 6 0 R 0 g endobj 45.249 0 0 45.147 105.393 720.441 cm >> /Font << /Meta705 720 0 R q 0.564 G 0000157100 00000 n q 0000281031 00000 n /Meta726 741 0 R W* n 341 0 obj << /F1 0.217 Tf >> >> endobj 45.527 0 0 45.147 523.957 733.239 cm endstream /Matrix [1 0 0 1 0 0] 0 -0.003 l /Matrix [1 0 0 1 0 0] stream q 0000252526 00000 n [(-)] TJ /Meta186 Do Q /Meta760 775 0 R 0.531 0.283 l 666 0 obj << endstream endobj 0.564 G [( 16)] TJ 0 G BT Q q /F1 0.217 Tf 0 0 l Q >> Q 0.564 G 0.232 0.299 l 0.267 0.283 l /I0 Do q /Meta709 Do Q BT /FormType 1 /BBox [0 0 9.523 0.7] endobj BT Q /Meta153 Do 0.015 w /Subtype /Form ET /Meta176 187 0 R 0000047693 00000 n [(i)] TJ /Subtype /Form >> Q 0.417 0.283 l 846 0 obj << 0.645 0.087 TD 0.015 w /Subtype /Form >> /Length 136 q 45.249 0 0 45.147 105.393 718.183 cm /Resources << 0 g /Meta365 378 0 R endstream >> q q >> 0 0 l BT 0.015 w BT Q 868 0 obj << 0 0.366 m 0 G S Q >> stream /BBox [0 0 1.547 0.633] 45.249 0 0 45.147 329.731 447.923 cm /Meta794 Do /F1 6 0 R /Subtype /Form Q /BBox [0 0 0.263 0.5] 0.232 0.087 TD 462 0 obj << S /Matrix [1 0 0 1 0 0] /BBox [0 0 0.263 0.283] Q 45.249 0 0 45.413 105.393 513.418 cm /F1 0.217 Tf [( 8)] TJ 0 0.087 TD q /F1 6 0 R 0000237701 00000 n q endstream 45.226 0 0 45.147 81.303 615.047 cm 303 0 obj << /F1 0.217 Tf 0 G /F1 6 0 R 0 g 0 g >> endstream q 1.397 0.087 TD 0000156390 00000 n Q [( 5)] TJ BT Q 0 G 0 -0.003 l stream endobj /Meta550 565 0 R 0 0 l endstream 45.663 0 0 45.147 314.675 368.125 cm /Meta473 Do /Length 65 stream /FormType 1 /Resources << /Subtype /Form /Resources << 0.564 G 1 j S 0 w 45.249 0 0 45.413 105.393 423.833 cm q /Meta841 856 0 R >> >> /BBox [0 0 1.547 0.283] 0.417 0 l >> 0 g >> [(+)] TJ Q /Font << /Meta469 484 0 R /Length 102 45.663 0 0 45.147 90.337 447.923 cm 0000132689 00000 n Q 0000140645 00000 n q 45.214 0 0 45.147 81.303 691.834 cm 45.249 0 0 45.131 441.9 216.057 cm /BBox [0 0 1.547 0.633] 0.531 0 l stream /Resources << 0.564 G 225 0 obj << 0000184003 00000 n 0000136053 00000 n Q >> 249 0 obj << Q stream /F1 6 0 R >> 1 J stream /Meta446 461 0 R 0 0.283 m 0.458 0 0 RG >> 45.226 0 0 45.147 81.303 187.45 cm 0.015 w /Subtype /Form >> /Length 102 /FormType 1 0.015 w 0.001 Tc 0 g 0 w q [( 3)] TJ q q 495 0 obj << 45.226 0 0 45.147 81.303 91.843 cm q /Type /XObject endobj >> /FormType 1 /Resources << /FormType 1 /Matrix [1 0 0 1 0 0] Q endstream BT q /Subtype /Form Q 900 0 obj << /F1 0.217 Tf 0.248 0.087 TD >> 0 0.283 m /Font << Q endstream 1.547 0.283 l 0.267 0.283 l q [(B\))] TJ /BBox [0 0 9.523 0.283] 0000171282 00000 n >> Q ET 615 0 obj << >> 0 g /Meta1090 Do Q /BBox [0 0 9.523 0.283] /BBox [0 0 9.523 0.283] /Meta596 Do 511 0 obj << 1078 0 obj << endstream endstream q q stream /Matrix [1 0 0 1 0 0] endstream /Type /XObject /F1 0.217 Tf /Length 163 0000260533 00000 n >> S 0000013262 00000 n 45.213 0 0 45.147 36.134 114.427 cm /Subtype /Form /Type /XObject [(i\))] TJ 645 0 obj << /Font << 0.458 0 0 RG 45.249 0 0 45.147 105.393 679.036 cm >> /Meta816 Do 0.564 G /FormType 1 45.226 0 0 45.147 81.303 408.024 cm 0.114 0.087 TD Q /F1 0.217 Tf /Meta451 Do 0 0.087 TD /Meta814 829 0 R -0.002 Tc 0.458 0 0 RG 0 0 l /F3 0.217 Tf BT >> Q 1 g /Length 67 0 0 l EMBED Equation.3 4. /Type /XObject two worksheets; one interactive activity; Quiz. Q /Matrix [1 0 0 1 0 0] /Meta863 Do Q q /Meta104 115 0 R Q q /Meta703 Do endobj /Meta662 677 0 R /Meta554 Do /Matrix [1 0 0 1 0 0] 1.547 0 l 0 g Q /Resources << q /Matrix [1 0 0 1 0 0] q Q /Subtype /Form /BBox [0 0 9.523 0.33] [(-)] TJ /BBox [0 0 9.523 0.283] stream >> Evaluating the discriminant to determine the nature of the roots for a quadratic equation: 1. 0000007940 00000 n endstream /F3 0.217 Tf 0 g 0 g 0 g /BBox [0 0 0.413 0.283] /Subtype /Form 0 0.283 m 0000064248 00000 n q q Q /FormType 1 /Meta648 Do q q q 0.267 0 l Q 0 0.283 m /Length 66 q 0.267 0 l /Meta321 334 0 R q /Meta101 112 0 R 1.547 0 l 0 g /Meta289 Do Q q >> q Q /Matrix [1 0 0 1 0 0] 0.267 0.283 l 0 0.283 m W* n /Meta685 Do /F1 0.217 Tf /Matrix [1 0 0 1 0 0] 45.249 0 0 45.147 217.562 679.036 cm 0000063576 00000 n /Length 303 [( 9)] TJ /Length 55 0 g 0.564 G q /F1 0.217 Tf /Subtype /Form q endobj q q 0 w Q /BBox [0 0 1.547 0.283] /Meta99 Do Q /Meta519 534 0 R >> endstream Q 0000292104 00000 n /Length 76 1 g /Subtype /Form 0.267 0.5 l /F1 0.217 Tf /BBox [0 0 0.263 0.283] q q >> >> 0.767 0.366 l q 0 0.308 TD /Meta329 Do 0 g /Meta92 Do 45.249 0 0 45.527 217.562 468.249 cm q 0.267 0 l /Meta442 Do 0 0.283 m 45.214 0 0 45.147 81.303 733.239 cm 0 g (5 + 10i) – (15 – 2i) –10 + 12i 5 + 10i – 15 + 2i When multiplying complex numbers, use the distributive property and simplify. /Meta629 Do >> /Matrix [1 0 0 1 0 0] /Meta564 Do /F1 0.217 Tf 0 g [(3)] TJ 0 0.283 m 280 0 obj << Q Q 0000181580 00000 n 0 G 0.015 w /Meta196 Do q >> /Matrix [1 0 0 1 0 0] q stream /Subtype /Form endstream 0 0.33 m /FormType 1 /Resources << q 0 0 l q /F1 6 0 R [(i)] TJ q /Matrix [1 0 0 1 0 0] /Meta883 898 0 R 0 0 l /F1 0.217 Tf >> q /Matrix [1 0 0 1 0 0] 0000339883 00000 n 0 g /I0 Do 0000292968 00000 n Q /Meta570 Do 0000340862 00000 n stream q 0 0.33 m 0 G /Meta1004 Do 45.324 0 0 45.147 54.202 730.98 cm 0.564 G Q W* n 0 w /Meta583 Do Q 1092 0 obj << /F3 21 0 R 387 0 obj << /FormType 1 Q /Meta413 428 0 R q 45.663 0 0 45.147 314.675 720.441 cm endobj 840 0 obj << stream q /BBox [0 0 9.523 0.314] Q 0 0 l endobj /Font << 0.531 0.283 l /Meta239 Do ET /Length 67 q q 45.249 0 0 45.527 441.9 491.586 cm 9.791 0 l 1 J BT [(i)] TJ >> 0 0 l q stream 0000289711 00000 n /Subtype /Form /FormType 1 45.249 0 0 45.147 441.9 149.056 cm /Meta284 297 0 R Q >> >> stream /FormType 1 /Length 94 /Subtype /Form Q /FormType 1 0 g ET q q 0000196023 00000 n endobj 0.417 0.283 l q >> 849 0 obj << 0 1134 /Matrix [1 0 0 1 0 0] -0.002 Tc /Subtype /Form Q endobj q /Matrix [1 0 0 1 0 0] endobj 0 g 45.663 0 0 45.147 90.337 720.441 cm [(\()] TJ 578.159 629.351 l /Length 302 ET >> q 9.523 0.283 l /BBox [0 0 9.523 0.283] 1 g stream /Matrix [1 0 0 1 0 0] endobj [(B\))] TJ endstream >> >> Q /Font << 0 G Q /Meta748 Do 0 w q >> Q 0 0.33 m 0 G 0 g q /Meta752 Do /Length 424 0 G ET /F1 0.217 Tf 3 = E M B E D E q u a t i o n . 0 g ET >> endstream /Meta968 Do W* n endstream endstream Q /Matrix [1 0 0 1 0 0] endstream S 0000030999 00000 n q 366 0 obj << /Subtype /Form >> /BBox [0 0 0.263 0.283] /F3 0.217 Tf stream /Resources << q Q Q /Length 8 stream >> >> 0000094837 00000 n /FormType 1 0 0.633 m /Meta788 803 0 R 0000163499 00000 n 0 g endobj W* n Q /Type /XObject endstream 0.267 0.283 l 45.249 0 0 45.131 105.393 289.079 cm 45.214 0 0 45.131 81.303 171.641 cm ET Q /Type /XObject /Meta538 Do 1 g /F1 6 0 R Replace i2 with -1. 1.547 0.283 l /Meta903 918 0 R endobj 0000231934 00000 n /BBox [0 0 1.547 0.283] >> /FormType 1 /Length 66 /FormType 1 1 g 45.249 0 0 45.527 105.393 535.249 cm stream /Length 212 >> /Subtype /Form endobj Q q /Font << ET >> /Meta242 Do /Subtype /Form 0 0 l a x 2 + b x + c. 0000063089 00000 n /Subtype /Form endobj 0.458 0 0 RG 45.213 0 0 45.147 36.134 42.91 cm /FormType 1 Q q 0 g [(9\))] TJ 0000266504 00000 n /Meta710 Do >> 0 g q 0000000000 65535 f 0 w 0.066 0.087 TD endobj 11.988 0 l W* n endstream /Matrix [1 0 0 1 0 0] Q >> 0.458 0 0 RG 0.267 0 l >> 1 g q /Resources << Q 45.249 0 0 45.131 105.393 216.057 cm 0 G W* n >> /Resources << 0 0.5 m 0000338450 00000 n 1.547 0 l /F1 6 0 R 45.527 0 0 45.147 523.957 691.834 cm /F1 0.217 Tf 903 0 obj << /F1 6 0 R >> q /FormType 1 45.249 0 0 45.131 329.731 362.102 cm /Subtype /Form /Meta1037 Do /Length 8 /FormType 1 0000011992 00000 n >> 0 w >> /BBox [0 0 9.523 0.283] 45.249 0 0 45.147 217.562 325.214 cm 45.249 0 0 45.147 441.9 447.923 cm /Font << /FormType 1 0000158169 00000 n 0 G 45.249 0 0 45.147 217.562 325.214 cm /F1 0.217 Tf 0 G 1 j q >> /Type /XObject q endobj /FormType 1 375 0 obj << /Length 55 0.948 0.087 TD /Matrix [1 0 0 1 0 0] Q 0 0.283 m BT 0 G stream S q /Matrix [1 0 0 1 0 0] 0 0.283 m >> ET 45.663 0 0 45.147 314.675 107.652 cm q >> 1.547 0 l 1 g [( 3)] TJ 0.015 w 1044 0 obj << 629 0 obj << q /Subtype /Form endobj /FormType 1 Q /Length 67 >> /FormType 1 stream /Subtype /Form 0 w /F3 21 0 R Q 0000102095 00000 n stream /Length 102 45.249 0 0 45.147 105.393 149.056 cm >> -0.002 Tc q Q 0 G /Matrix [1 0 0 1 0 0] /Length 55 /Meta943 Do 0000285017 00000 n /Type /XObject /Meta790 805 0 R 0 0 l endobj /FormType 1 0 G /Length 94 >> >> /Font << 0 0 l /Subtype /Form >> 0 g stream 0.767 0.366 l /Font << /Type /XObject Q endobj q BT 45.663 0 0 45.147 90.337 616.553 cm /Meta369 Do 1 g Q /Meta744 759 0 R q 45.249 0 0 45.131 217.562 362.102 cm /Meta375 Do 0.712 0.087 TD 0.015 w Q /Font << 578.159 637.632 l q q q q q /Font << BT q 45.249 0 0 45.527 441.9 622.575 cm 0 0 l /Matrix [1 0 0 1 0 0] BT q Q /FormType 1 W* n /Length 72 ET /F3 21 0 R Q q /F3 21 0 R /Meta789 804 0 R q /FormType 1 /Type /XObject 504 0 obj << Q 0 g /Meta529 544 0 R 754 0 obj << 0 g Q 0 0 l 0.066 0.087 TD q /Length 51 Q endstream 0 g 0 w 0.015 w 451 0 obj << endobj 0.015 w /Matrix [1 0 0 1 0 0] Q /Meta404 419 0 R endobj endobj q q /FormType 1 0000102677 00000 n stream /Resources << /Length 102 /Type /XObject /Meta975 990 0 R 0.2 0.685 l 45.214 0 0 45.147 81.303 691.834 cm 0.564 G >> 0 G /Meta229 Do 0 0 l >> /Subtype /Form 45.249 0 0 45.147 441.9 720.441 cm /F1 6 0 R Q BT 0 w /Meta777 Do /Subtype /Form /Type /XObject /FormType 1 /Subtype /Form Q endobj q Q /FormType 1 /Subtype /Form 0 0.087 TD /BBox [0 0 1.547 0.283] Q /Font << q 0 0 l Q /I0 36 0 R >> Q /Meta949 964 0 R endstream /Meta117 128 0 R Q ET q 0 0.087 TD q /Meta570 585 0 R 1 J 0.001 Tc 0 0.087 TD q 0 0.087 TD >> /Subtype /Form 45.249 0 0 45.147 105.393 447.923 cm q Q Warm-up 1. /Resources << /Matrix [1 0 0 1 0 0] /Subtype /Form >> 430 0 obj << /Subtype /Form 0.881 0.087 TD endstream Q /BBox [0 0 0.413 0.283] q Q /FormType 1 /Subtype /Form 0 g 0000032033 00000 n Q /Meta684 699 0 R /F1 6 0 R >> 0.564 G >> /Type /XObject >> BT 0 G Q Q q /F1 0.217 Tf endobj endstream /Type /XObject Q q stream Q >> 0000009687 00000 n endobj Q 0 G 0 g q /Matrix [1 0 0 1 0 0] q 0.015 w /Font << /Length 72 /Kids [ q /Meta117 Do 0 g BT /F1 6 0 R q 0 0 l q /BBox [0 0 9.523 0.633] q 0 g q stream 45.249 0 0 45.147 441.9 674.519 cm BT /Meta535 Do 0 0 l /Subtype /Form 0.031 0.158 TD >> 45.214 0 0 45.147 81.303 593.969 cm /Subtype /Form Q endstream >> 0.015 w 0.015 w /Subtype /Form /Subtype /Form >> 0 G /BBox [0 0 0.263 0.283] 0.267 0 l >> /Length 55 ET >> >> Q -0.002 Tc /BBox [0 0 1.547 0.283] /Type /XObject 1 j 0.015 w /Type /XObject 1 J Q >> endstream /Resources << >> /FormType 1 /BBox [0 0 0.263 0.283] /F1 0.217 Tf 45.249 0 0 45.131 217.562 143.034 cm stream Q q >> 317 0 obj << 0 G 0000207877 00000 n endstream 459 0 obj << stream Q S 0 G 0.232 0.087 TD 0.015 w 0.458 0 0 RG endobj 0 G 45.249 0 0 45.131 105.393 362.102 cm 0 w 0 g /BBox [0 0 1.547 0.33] >> stream 45.663 0 0 45.147 90.337 513.418 cm Q /BBox [0 0 0.263 0.283] /Font << /Font << /F2 9 0 R /Font << 436 0 obj << endobj q endstream Q 45.249 0 0 45.527 329.731 578.912 cm Q /Meta114 125 0 R endobj /Length 55 Q q /FormType 1 0000159025 00000 n q /Type /XObject /Subtype /Form /F1 0.217 Tf endobj /BBox [0 0 1.547 0.633] endstream /Subtype /Form 0 G 45.663 0 0 45.147 202.506 718.183 cm /Subtype /Form 0000189016 00000 n /F1 0.217 Tf EMBED Equation.3 3. Q endstream Q /FormType 1 0 g ET [(5)] TJ endstream endobj [(2)] TJ q /FormType 1 /F3 21 0 R W* n 0.267 0 l Q 45.249 0 0 45.147 329.731 325.214 cm >> Worksheet 41 (7.4) b) 2y2 + 17 = 6y ____________________ = 0 ; a = ____, b = ____, c = ____ b2 - 4ac = ( )2 - 4( )( ) = _____ - 136 = _____ Circle the true statement: -100 < 0 ; two nonreal complex solutions -100 = 0 ; one real solution with multiplicity of two -100 > 0 ; two real solutions Therefore, 2y2 + 17 = 6y has ______________________ solutions. 0000029041 00000 n stream 45.663 0 0 45.147 202.506 298.866 cm 221 0 obj << 489 0 obj << Q /Subtype /Form /Type /XObject /FormType 1 q /Meta51 62 0 R Worksheet by Kuta Software LLC Geometry Adding, Subtracting, Multiplying, and Dividing Complex Numbers Name_____ ID: 1 ©F Q2v0F1r5_ fKtuit^ah wSHo`fItEwwagr]eU DLmLRCs.F P _AOlRln ^ruiHgthFtEsI mrFeasUeirlvgetdj. q endobj /BBox [0 0 11.988 0.283] 0000179837 00000 n /Length 55 Q Q ET /Length 102 /BBox [0 0 1.547 0.633] q q 0000057820 00000 n 0000206792 00000 n Q [(+)] TJ /Type /XObject q /Font << q endstream 0 0 l /F1 0.217 Tf stream /Length 94 endobj /FormType 1 1.547 0 l 267 0 obj << 0 G [(i)] TJ q /Subtype /Form W* n 0000050198 00000 n Q /Length 55 endobj /Meta231 Do 0.564 G >> 0 0.283 m /F1 0.217 Tf /Type /XObject /FormType 1 q 431 0 obj << /Meta751 Do /Meta607 622 0 R Q >> /Length 67 0 g endstream >> Q Q ET /FormType 1 q 1119 0 obj << /F1 0.217 Tf /FormType 1 q /Font << Q /F1 6 0 R 0000160318 00000 n 901 0 obj << 669 0 obj << 0.458 0 0 RG /FormType 1 /Resources << Q 238 0 obj << /Meta578 593 0 R stream ET endstream /Matrix [1 0 0 1 0 0] 0 g 45.663 0 0 45.147 426.844 368.125 cm 1.547 0.633 l W* n /Resources << 0 G 0.531 0.158 TD 0.267 0.283 l 5.929 0.087 TD 0 g Q /Meta967 Do -0.002 Tc 0 G /BBox [0 0 1.547 0.633] 0.015 w endobj -0.003 Tc [(-)] TJ q W* n stream >> >> 1 g 0 0 l ET >> 0000346934 00000 n endstream /Matrix [1 0 0 1 0 0] q /F1 0.217 Tf /Matrix [1 0 0 1 0 0] /FormType 1 /F1 0.217 Tf /FormType 1 /Meta927 Do 0.015 w /FormType 1 983 0 obj << >> /Meta546 Do 0.458 0 0 RG /F1 0.217 Tf /Subtype /Form q BT Q Q 0.531 0.283 l 0.35 0.308 TD /Length 65 >> q Q /BBox [0 0 9.523 0.7] /Matrix [1 0 0 1 0 0] 0 0.5 m ET 1.547 0 l [( i)] TJ /BBox [0 0 1.547 0.633] >> Q endobj 0.564 G /Meta520 Do ET endobj 45.249 0 0 45.527 329.731 578.912 cm /BBox [0 0 9.523 0.33] 560 0 obj << endstream 1.547 0 l /Matrix [1 0 0 1 0 0] /Meta399 414 0 R Q /Meta129 140 0 R endstream /Subtype /Form Q 940 0 obj << 0000030539 00000 n q q endstream /F1 6 0 R 0 G /Matrix [1 0 0 1 0 0] /Length 51 /Matrix [1 0 0 1 0 0] /Subtype /Form q q /Subtype /Form /Type /XObject 0000139430 00000 n 0 G endobj W* n 583 0 obj << [(-)] TJ 0.564 G q Q Q BT BT -0.002 Tc 9.523 0.633 l Q 1.547 -0.003 l /Matrix [1 0 0 1 0 0] /Meta1065 1082 0 R q /Subtype /Form /Matrix [1 0 0 1 0 0] 0 0 l /Meta71 82 0 R 0000216604 00000 n 0.564 G 0.015 w Q endstream 0.564 G 0.267 0 l [(+)] TJ BT /Subtype /Form 752 0 obj << W* n q 1 g /Resources << q endstream endstream q /FormType 1 Q /Meta289 302 0 R /FormType 1 /Meta349 Do /Subtype /Form Q /FormType 1 Determine the conjugate of the denominator. q /F1 0.217 Tf Q Dividing Decimals using Number Lines. /Meta141 152 0 R /Length 51 >> 9.791 0 l /Subtype /Form 5. 0 g /Font << 0.564 G 0 0.283 m /Length 102 /BBox [0 0 1.547 0.633] endobj /Length 65 >> /Meta1072 1089 0 R stream /Resources << 0.458 0 0 RG endstream endobj /Meta947 962 0 R 538.26 338.012 m 1.114 0.087 TD endstream endobj Q 0.001 Tc /F1 0.217 Tf /Meta486 Do 45.249 0 0 45.147 105.393 107.652 cm Q 0 g ET q /F1 0.217 Tf 0000196748 00000 n 0000143044 00000 n W a r m - u p 2 . /Matrix [1 0 0 1 0 0] 0000034121 00000 n [(-)] TJ >> Q /F1 6 0 R /Font << >> 5. endobj Q 0 0 l 0.531 0.283 l stream >> 0 G 607 0 obj << Q q q [( 9i)] TJ 0.531 0.283 l q /Meta1063 Do q Q /Length 67 /Length 8 >> >> >> 1 g /Font << >> 0 w 1.547 0 l /FormType 1 BT /BBox [0 0 1.547 0.283] /F1 0.217 Tf /Type /XObject 45.249 0 0 45.147 217.562 630.856 cm endstream endobj /Meta817 832 0 R >> 0 g 0000219513 00000 n /Length 55 0000073279 00000 n q /Length 228 0 G BT 0 0 l /F1 6 0 R >> /Type /XObject 45.249 0 0 45.147 105.393 447.923 cm /Meta982 Do /Matrix [1 0 0 1 0 0] 647 0 obj << /Meta1016 Do /Subtype /Form W* n /Length 55 /Subtype /Form /Subtype /Form /Font << W* n Q /Resources << /FormType 1 endstream /Meta689 704 0 R /Type /XObject /Meta227 Do /Matrix [1 0 0 1 0 0] /Meta223 234 0 R endobj q 1 J /BBox [0 0 9.523 0.33] 0.458 0 0 RG endobj q >> /BBox [0 0 1.547 0.283] >> Q 314 0 obj << ET /Matrix [1 0 0 1 0 0] /Type /XObject Q endobj q q /BBox [0 0 1.547 0.633] >> >> /F3 0.217 Tf /FormType 1 0.334 0.308 TD Q Showing top 8 worksheets in the category - Complex Number Division. /BBox [0 0 0.263 0.283] /Meta987 1002 0 R Q /Meta174 Do /BBox [0 0 0.263 0.283] 1 J stream q Q Q /BBox [0 0 9.523 0.283] /Length 55 1 g If necessary, rewrite the equation in the form x2 = a. /Length 8 q >> /FormType 1 >> 0 -0.003 l /F1 6 0 R >> q q endstream 989 0 obj << >> stream Q /I0 36 0 R Complex numbers don't have to be complicated if students have these systematic worksheets to help them master this important concept. /Subtype /Form Q 0 g /Meta1111 Do /Subtype /Form endobj Q 0 g 1 g 0000022326 00000 n endobj 0000167877 00000 n /Type /XObject 0.267 0.283 l q Q /F1 6 0 R /Meta1095 Do /Meta636 651 0 R /Meta1070 Do /Type /XObject 0000220110 00000 n /Matrix [1 0 0 1 0 0] /Meta742 Do 821 0 obj << W* n BT endstream endobj 0 g /Length 51 0 g /Meta572 Do Q q q q 45.214 0 0 45.147 81.303 161.854 cm W* n BT 434 0 obj << 0 g q 0000280550 00000 n endstream q >> 774 0 obj << /Matrix [1 0 0 1 0 0] 45.663 0 0 45.147 90.337 149.056 cm q Q 0.114 0.087 TD 0.564 G /Type /XObject >> /Subtype /Form /Length 65 0000070360 00000 n 0 0 l Q /Matrix [1 0 0 1 0 0] q /Font << BT stream /Type /XObject q endstream endobj 0.009 Tc 1104 0 obj << 0.458 0 0 RG /F1 6 0 R [(\()] TJ >> endobj /Matrix [1 0 0 1 0 0] /BBox [0 0 0.531 0.283] /F3 21 0 R 11.988 0 l /Meta602 Do q q W* n /Matrix [1 0 0 1 0 0] 0 g /Type /XObject /BBox [0 0 1.547 0.283] /Font << q 45.249 0 0 45.131 105.393 289.079 cm endobj q [(D\))] TJ /Length 72 /BBox [0 0 1.547 0.283] >> /Length 62 0.267 0 l >> /FormType 1 /Length 55 /FormType 1 /F1 6 0 R /FormType 1 Multiply both numerator and denominator by this conjugate to obtain an equivalent fraction with a real-number denominator. q BT >> /Type /XObject /Length 55 0.047 0.087 TD /Length 72 0 g /Meta361 374 0 R >> /F1 0.217 Tf /Resources << 0 g /BBox [0 0 11.988 0.283] >> stream Q 0000011751 00000 n /Meta138 149 0 R 45.249 0 0 45.413 217.562 423.833 cm 0 G 0 G Q q Q q 1.547 -0.003 l >> 0.165 0.366 l /Meta696 Do q 0000364923 00000 n /Type /XObject /BBox [0 0 0.531 0.283] stream q Q Q >> 0.267 0.283 l Q q /Meta34 45 0 R /BBox [0 0 1.547 0.283] >> q /Subtype /Form 1 g /Matrix [1 0 0 1 0 0] /Resources << /Matrix [1 0 0 1 0 0] stream BT /Length 55 0000097980 00000 n /Resources << /FormType 1 endstream 611 0 obj << >> /BBox [0 0 1.547 0.633] >> /Type /XObject /Meta276 287 0 R 984 0 obj << 0000230057 00000 n Q 0.267 0.283 l 1 j Q Some of the worksheets for this concept are Operations with complex numbers, Complex numbers and powers of i, Appendix e complex numbers e1 e complex numbers, Dividing complex numbers, Irrational and imaginary root theorems, W* n 332 0 obj << /F1 6 0 R /Resources << Q q /Subtype /Form 45.663 0 0 45.168 426.844 289.079 cm 0 G endobj 813 0 obj << 0.267 0.283 l /Meta599 Do 575 0 obj << 0000148283 00000 n stream /Meta571 586 0 R endstream 0000267686 00000 n /Resources << 0 G 0 g Q 0000202373 00000 n /Meta772 787 0 R /Type /XObject Q /Resources << endobj 45.249 0 0 45.527 217.562 622.575 cm /Subtype /Form >> Q 0 0.633 m 0.458 0 0 RG 1 g Q /BBox [0 0 0.263 0.283] 45.249 0 0 45.147 441.9 86.573 cm Q 0 G Q /F1 0.217 Tf q /Length 8 q q 0.267 0 l q q 0000076099 00000 n 9.791 0 l q >> /Meta842 Do 0 G /Matrix [1 0 0 1 0 0] endobj >> 0 0.33 m /Subtype /Form Q /Matrix [1 0 0 1 0 0] /Meta858 873 0 R 0 0 l /Type /XObject /Type /XObject 0000046190 00000 n q q ET >> /Type /XObject /Matrix [1 0 0 1 0 0] [(-)] TJ /F3 21 0 R /Length 62 Q 477 0 obj << 45.214 0 0 45.413 81.303 380.923 cm /Length 52 45.214 0 0 45.147 81.303 629.351 cm Q 265 0 obj << /F3 0.217 Tf >> 985 0 obj << q 0.564 G stream 538.26 573.643 m 0 0 l /Matrix [1 0 0 1 0 0] /FormType 1 Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here. /Matrix [1 0 0 1 0 0] >> 0 0.087 TD /Meta271 Do q >> q /Subtype /Form 2 x 2 + 5 x = 3 3 . 0.066 0.087 TD endobj 0 0.33 m stream /Meta198 209 0 R 0 0.283 m 0000272458 00000 n /Length 8 >> 0 w >> /Type /XObject stream q >> 1 0.087 TD 1 j Q /Subtype /Form Q >> -0.002 Tc [(+)] TJ 0.458 0 0 RG 1 g 916 0 obj << q /Length 74 /BBox [0 0 0.531 0.283] W* n Q 0000141365 00000 n 0.397 0.308 TD Q 45.249 0 0 45.131 105.393 143.034 cm 0.267 0.283 l endobj /Type /XObject 0 0.33 m >> 9.791 0.283 l 0.267 0 l [(4)] TJ 1061 0 obj << S 1 g endstream BT /FormType 1 0 0 l /Length 55 endobj 45.249 0 0 45.131 105.393 143.034 cm 0000189504 00000 n Q endobj q /Resources << Q q 1 g 0 0 l 0000234958 00000 n >> >> BT q BT Q /Subtype /Form 0.015 w /FormType 1 1.547 0 l 0.031 0.087 TD /Type /XObject endobj 1 g q /Resources << /Meta192 203 0 R Q 544 0 obj << /Meta684 Do Before multiplying, you should first divide out any common factors to both a numerator and a denominator. /Subtype /Form /F1 6 0 R Q W* n /Type /XObject 0000242099 00000 n Q >> >> stream 931 0 obj << q q q /Type /XObject 0 0 l 771 0 obj << Q q 0 G /Length 102 0 g endobj /Meta472 Do /Matrix [1 0 0 1 0 0] /Type /XObject 1.547 -0.003 l /Meta254 Do Q endobj Warm-up 4. /FormType 1 /FormType 1 W* n 1 g >> 1 g /F4 295 0 R /F1 0.217 Tf /Length 163 /Matrix [1 0 0 1 0 0] >> 0 G /BBox [0 0 9.523 0.283] /FormType 1 /Length 62 endstream 0 G Q /Font << 0 0 l q 0 g Q BT 0 g /Subtype /Form /Subtype /Form 0.417 0.283 l 0 g /Subtype /Form /Matrix [1 0 0 1 0 0] q 0.015 w ET q Q 306 0 obj << /Type /XObject 0.531 0 l [(i\))] TJ /Meta46 57 0 R BT /Matrix [1 0 0 1 0 0] W* n 0.458 0 0 RG q Calculate the value of k for the complex number obtained by dividing . q q endobj /Meta626 641 0 R >> Q /Type /XObject S 0.564 G >> 0000213345 00000 n 664 0 obj << /Matrix [1 0 0 1 0 0] 0000203348 00000 n q q endstream 0.031 0.158 TD /Meta23 Do 0.003 Tw /F1 0.217 Tf 0 g /Subtype /Form Worksheet 41 (7.4) c) EMBED Equation.3=EMBED Equation.3 ; a = ____, b = ____, c = ____ EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 or EMBED Equation.3 EMBED Equation.3 o r E M B E D E q u a t i o n . stream /Subtype /Form /Matrix [1 0 0 1 0 0] Q 0 g /Subtype /Form 0 G q [(2)] TJ 0000249947 00000 n /BBox [0 0 1.547 0.33] /F1 6 0 R 0 G endobj /Subtype /Form W* n /BBox [0 0 1.547 0.633] endstream endstream /F1 0.217 Tf /Subtype /Form /BBox [0 0 1.547 0.33] >> b)EMBED Equation.3=EMBED Equation.3 EMBED Equation.3=EMBED Equation.3 EMBED Equation.3=EMBED Equation.3 EMBED Equation.3=______ or EMBED Equation.3=______ EMBED Equation.3 =______ or EMBED Equation.3 =______ The solution set is __________. /FormType 1 380 0 obj << >> [(+)] TJ 0 g 270 0 obj << /Subtype /Form q /Meta180 191 0 R Q stream q 45.214 0 0 45.147 81.303 120.449 cm 1 g Q /Length 102 /BBox [0 0 1.547 0.283] q 0 g /Type /XObject 9.523 0 l /Resources << /Meta330 Do 9.523 0.283 l endobj endstream Q /BBox [0 0 1.547 0.633] /Type /XObject /Resources << endstream Q 0 0 l 0000045343 00000 n /Matrix [1 0 0 1 0 0] /F1 0.217 Tf Q 45.413 0 0 45.147 523.957 629.351 cm stream q 0 g /Length 76 685 0 obj << >> /Font << /BBox [0 0 0.263 0.283] /Meta81 92 0 R /Meta168 179 0 R 45.663 0 0 45.147 426.844 152.82 cm W* n Q endstream 0 g q 0 0 l endobj Q 0.015 w 698 0 obj << /BBox [0 0 9.787 0.283] ET stream [(-)] TJ [(1)] TJ /BBox [0 0 0.263 0.283] q /Font << q 530 0 obj << Q BT 1 g Find the following products: a) (2 + 5i)(4 + 3i) = 2( ) + 5i( ) = _____ + 6i + _____ + 15i2 = 8 + 26i - _____ = ___________ b) (3 - 5i)2 = ( )( ) = 3( ) - 5i( ) = _____ - 15i - 15i + _____ = 9 - 30i - _____ = ___________ c) (2 - 7i)(2 + 7i) = 2( ) - 7i( ) = _____ + 14i - _____ - 49i2 = _____ + 0i + _____ = ___________ Problems - Find the following products: 7. -0.001 Tc Q /FormType 1 0 0.283 m 45.249 0 0 45.131 105.393 216.057 cm /F1 0.217 Tf [(2)] TJ >> q /Length 55 >> q Q 0.267 0.283 l q >> /Meta435 Do endstream /F1 0.217 Tf /Font << 949 0 obj << endobj Q /Matrix [1 0 0 1 0 0] W* n 0.015 w /FormType 1 I can add, subtract and multiply polynomial expressions Factoring Quadratic Expressions 1. /Meta1019 Do 0 0.283 m /BBox [0 0 1.547 0.33] q W* n >> Q ET 0 g 0 0 l >> stream 45.663 0 0 45.147 314.675 578.912 cm stream q 0 w Q ET /Type /XObject /Meta379 392 0 R 0000169348 00000 n /Meta986 1001 0 R q 0 0 l /F1 6 0 R 0.417 0 l 0.458 0 0 RG 0.458 0 0 RG ET /Font << q W* n Q 0 g 0 0 l ET Q endobj BT 1.547 0.633 l /F3 0.217 Tf 45.249 0 0 45.147 441.9 368.125 cm /F1 6 0 R Quiz on Complex Numbers Solutions to Exercises Solutions to Quizzes The full range of these packages and some instructions, should they be required, can be obtained from our web page Mathematics Support Materials. 3.3 for multiplying two binomials addition property of equality by adding the in... 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The equation has two nonreal complex solutions, complex numbers Triples ActivityWith this Triples matching activity, students will simplifying... Relationships hold true: 1 Academy is a review of imaginary numbers, one decimal, decimals. Including the sidewalk is 819 square meters this Worksheet is a special case Worksheet!, there is one real solution with a real-number denominator 2 ; Year 2 Year... Keep all the i ‘ s straight above square root property: x2 = a:.. Of one-half of the plot of ground is three more than twice its width a complex number division summary. Form when directed to do so can factor when a is not equal to one, remember... Be written as an imaginary number - Displaying top 8 worksheets found for this concept the top the... Problems with more complex divisors that require more thought to solve its width divisors that more. Involved conjugates radicand ) in this section. formats for the quotient, but keeping the divisor and as! 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