Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ a c b d a d b c 2 2 2 2 2 2 2 2 2 2 2 c d 2 2 2 c d a c d b c d 2 2 2 2 2 2 2 2 2 2 c d a b 2 2 2 c d a c b d 2 2 2 2 Hence, proved. Question 5: Convert the following in the polar form: 1 7 i (i) 2 , (ii) 2 i Solution 5: (i) Here, z 1 7i 2 2 i 1 7i 1 7i 1 7i 4 i 4i 4 1 4i 2 i 2 2 1 7i 3 4i 3 4i 21i 28i 2 2 3 4i 3 4i 3 4 3 4 i 21 i 28 25 25 i 1 i 2 2 3 4 25 Let r cos 1 and rsin 1 On squaring and adding, we obtain 2 2 2 r r r 2 cos sin 2 2 2 2 cos 1 and 2 sin 1 1 3i 1 2i 2 2 2 2 r cos sin 1 2 2 cos sin 1 [Conventionally, r 0 ]

Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ cos 1 2 and 3 4 4 z r cos i r sin sin 3 3 3 3 2 cos i 2 sin 2 cos isin 4 4 4 4 This is the required polar form. 1 3i (ii) Here, z 1 2i 13i 12i 12i 12i 1 2i 3i 6 1 4 55i 1 i 5 Let r cos 1 and r sin 1 on squaring and adding, we obtain **11** 2 2 2 r r r 2 cos sin 2 2 2 2 cos 1 cos 1 2 and 3 4 4 and z r cos i r sin sin 1 2 2 sin 1 1 2 [As lies in II quadrant] 2 2 2 r cos sin 3 3 3 3 2 cos i 2 sin 2 cos isin 4 4 4 4 This is the required polar form. 2 2 cos sin 1 Conventionally, r 0 [As lies in II quadrant]

- Page 1 and 2:
Class XI Chapter 1 - Sets Maths ___

- Page 3 and 4:
Class XI Chapter 1 - Sets Maths ___

- Page 5 and 6:
Class XI Chapter 1 - Sets Maths ___

- Page 7 and 8:
Class XI Chapter 1 - Sets Maths ___

- Page 9 and 10:
Class XI Chapter 1 - Sets Maths ___

- Page 11 and 12:
Class XI Chapter 1 - Sets Maths ___

- Page 13 and 14:
Class XI Chapter 1 - Sets Maths ___

- Page 15 and 16:
Class XI Chapter 1 - Sets Maths ___

- Page 17 and 18:
Class XI Chapter 1 - Sets Maths ___

- Page 19 and 20:
Class XI Chapter 1 - Sets Maths ___

- Page 21 and 22:
Class XI Chapter 1 - Sets Maths ___

- Page 23 and 24:
Class XI Chapter 1 - Sets Maths ___

- Page 25 and 26:
Class XI Chapter 1 - Sets Maths ___

- Page 27 and 28:
Class XI Chapter 1 - Sets Maths ___

- Page 29 and 30:
Class XI Chapter 1 - Sets Maths ___

- Page 31 and 32:
Class XI Chapter 1 - Sets Maths ___

- Page 33 and 34:
Class XI Chapter 1 - Sets Maths ___

- Page 35 and 36:
Class XI Chapter 1 - Sets Maths ___

- Page 37 and 38:
Class XI Chapter 1 - Sets Maths ___

- Page 39 and 40:
Class XI Chapter 1 - Sets Maths ___

- Page 41 and 42:
Class XI Chapter 1 - Sets Maths ___

- Page 43 and 44:
Class XI Chapter 2 - Relations and

- Page 45 and 46:
Class XI Chapter 2 - Relations and

- Page 47 and 48:
Class XI Chapter 2 - Relations and

- Page 49 and 50:
Class XI Chapter 2 - Relations and

- Page 51 and 52:
Class XI Chapter 2 - Relations and

- Page 53 and 54:
Class XI Chapter 2 - Relations and

- Page 55 and 56:
Class XI Chapter 2 - Relations and

- Page 57 and 58:
Class XI Chapter 2 - Relations and

- Page 59 and 60:
Class XI Chapter 2 - Relations and

- Page 61 and 62:
Class XI Chapter 3 - Trigonometric

- Page 63 and 64:
Class XI Chapter 3 - Trigonometric

- Page 65 and 66:
Class XI Chapter 3 - Trigonometric

- Page 67 and 68:
Class XI Chapter 3 - Trigonometric

- Page 69 and 70:
Class XI Chapter 3 - Trigonometric

- Page 71 and 72:
Class XI Chapter 3 - Trigonometric

- Page 73 and 74:
Class XI Chapter 3 - Trigonometric

- Page 75 and 76:
Class XI Chapter 3 - Trigonometric

- Page 77 and 78:
Class XI Chapter 3 - Trigonometric

- Page 79 and 80:
Class XI Chapter 3 - Trigonometric

- Page 81 and 82:
Class XI Chapter 3 - Trigonometric

- Page 83 and 84:
Class XI Chapter 3 - Trigonometric

- Page 85 and 86:
Class XI Chapter 3 - Trigonometric

- Page 87 and 88:
Class XI Chapter 3 - Trigonometric

- Page 89 and 90:
Class XI Chapter 3 - Trigonometric

- Page 91 and 92: Class XI Chapter 3 - Trigonometric
- Page 93 and 94: Class XI Chapter 3 - Trigonometric
- Page 95 and 96: Class XI Chapter 3 - Trigonometric
- Page 97 and 98: Class XI Chapter 3 - Trigonometric
- Page 99 and 100: Class XI Chapter 4 - Principle of M
- Page 101 and 102: Class XI Chapter 4 - Principle of M
- Page 103 and 104: Class XI Chapter 4 - Principle of M
- Page 105 and 106: Class XI Chapter 4 - Principle of M
- Page 107 and 108: Class XI Chapter 4 - Principle of M
- Page 109 and 110: Class XI Chapter 4 - Principle of M
- Page 111 and 112: Class XI Chapter 4 - Principle of M
- Page 113 and 114: Class XI Chapter 4 - Principle of M
- Page 115 and 116: Class XI Chapter 4 - Principle of M
- Page 117 and 118: Class XI Chapter 4 - Principle of M
- Page 119 and 120: Class XI Chapter 4 - Principle of M
- Page 121 and 122: Class XI Chapter 4 - Principle of M
- Page 123 and 124: Class XI Chapter 4 - Principle of M
- Page 125 and 126: Class XI Chapter 5 - Complex Number
- Page 127 and 128: Class XI Chapter 5 - Complex Number
- Page 129 and 130: Class XI Chapter 5 - Complex Number
- Page 131 and 132: Class XI Chapter 5 - Complex Number
- Page 133 and 134: Class XI Chapter 5 - Complex Number
- Page 135 and 136: Class XI Chapter 5 - Complex Number
- Page 137 and 138: Class XI Chapter 5 - Complex Number
- Page 139 and 140: Class XI Chapter 5 - Complex Number
- Page 141: Class XI Chapter 5 - Complex Number
- Page 145 and 146: Class XI Chapter 5 - Complex Number
- Page 147 and 148: Class XI Chapter 5 - Complex Number
- Page 149 and 150: Class XI Chapter 5 - Complex Number
- Page 151 and 152: Class XI Chapter 5 - Complex Number
- Page 153 and 154: Class XI Chapter 5 - Complex Number
- Page 155 and 156: Class XI Chapter 6 - Linear Inequal
- Page 157 and 158: Class XI Chapter 6 - Linear Inequal
- Page 159 and 160: Class XI Chapter 6 - Linear Inequal
- Page 161 and 162: Class XI Chapter 6 - Linear Inequal
- Page 163 and 164: Class XI Chapter 6 - Linear Inequal
- Page 165 and 166: Class XI Chapter 6 - Linear Inequal
- Page 167 and 168: Class XI Chapter 6 - Linear Inequal
- Page 169 and 170: Class XI Chapter 6 - Linear Inequal
- Page 171 and 172: Class XI Chapter 6 - Linear Inequal
- Page 173 and 174: Class XI Chapter 6 - Linear Inequal
- Page 175 and 176: Class XI Chapter 6 - Linear Inequal
- Page 177 and 178: Class XI Chapter 6 - Linear Inequal
- Page 179 and 180: Class XI Chapter 6 - Linear Inequal
- Page 181 and 182: Class XI Chapter 6 - Linear Inequal
- Page 183 and 184: Class XI Chapter 6 - Linear Inequal
- Page 185 and 186: Class XI Chapter 6 - Linear Inequal
- Page 187 and 188: Class XI Chapter 6 - Linear Inequal
- Page 189 and 190: Class XI Chapter 6 - Linear Inequal
- Page 191 and 192: Class XI Chapter 6 - Linear Inequal
- Page 193 and 194:
Class XI Chapter 6 - Linear Inequal

- Page 195 and 196:
Class XI Chapter 6 - Linear Inequal

- Page 197 and 198:
Class XI Chapter 7 - Permutation an

- Page 199 and 200:
Class XI Chapter 7 - Permutation an

- Page 201 and 202:
Class XI Chapter 7 - Permutation an

- Page 203 and 204:
Class XI Chapter 7 - Permutation an

- Page 205 and 206:
Class XI Chapter 7 - Permutation an

- Page 207 and 208:
Class XI Chapter 7 - Permutation an

- Page 209 and 210:
Class XI Chapter 7 - Permutation an

- Page 211 and 212:
Class XI Chapter 7 - Permutation an

- Page 213 and 214:
Class XI Chapter 7 - Permutation an

- Page 215 and 216:
Class XI Chapter 7 - Permutation an

- Page 217 and 218:
Class XI Chapter 7 - Permutation an

- Page 219 and 220:
Class XI Chapter 8 - Binomial Theor

- Page 221 and 222:
Class XI Chapter 8 - Binomial Theor

- Page 223 and 224:
Class XI Chapter 8 - Binomial Theor

- Page 225 and 226:
Class XI Chapter 8 - Binomial Theor

- Page 227 and 228:
Class XI Chapter 8 - Binomial Theor

- Page 229 and 230:
Class XI Chapter 8 - Binomial Theor

- Page 231 and 232:
Class XI Chapter 8 - Binomial Theor

- Page 233 and 234:
Class XI Chapter 8 - Binomial Theor

- Page 235 and 236:
Class XI Chapter 8 - Binomial Theor

- Page 237 and 238:
Class XI Chapter 8 - Binomial Theor

- Page 239 and 240:
Class XI Chapter 8 - Binomial Theor

- Page 241 and 242:
Class XI Chapter 9 - Sequences and

- Page 243 and 244:
Class XI Chapter 9 - Sequences and

- Page 245 and 246:
Class XI Chapter 9 - Sequences and

- Page 247 and 248:
Class XI Chapter 9 - Sequences and

- Page 249 and 250:
Class XI Chapter 9 - Sequences and

- Page 251 and 252:
Class XI Chapter 9 - Sequences and

- Page 253 and 254:
Class XI Chapter 9 - Sequences and

- Page 255 and 256:
Class XI Chapter 9 - Sequences and

- Page 257 and 258:
Class XI Chapter 9 - Sequences and

- Page 259 and 260:
Class XI Chapter 9 - Sequences and

- Page 261 and 262:
Class XI Chapter 9 - Sequences and

- Page 263 and 264:
Class XI Chapter 9 - Sequences and

- Page 265 and 266:
Class XI Chapter 9 - Sequences and

- Page 267 and 268:
Class XI Chapter 9 - Sequences and

- Page 269 and 270:
Class XI Chapter 9 - Sequences and

- Page 271 and 272:
Class XI Chapter 9 - Sequences and

- Page 273 and 274:
Class XI Chapter 9 - Sequences and

- Page 275 and 276:
Class XI Chapter 9 - Sequences and

- Page 277 and 278:
Class XI Chapter 9 - Sequences and

- Page 279 and 280:
Class XI Chapter 9 - Sequences and

- Page 281 and 282:
Class XI Chapter 9 - Sequences and

- Page 283 and 284:
Class XI Chapter 9 - Sequences and

- Page 285 and 286:
Class XI Chapter 9 - Sequences and

- Page 287 and 288:
Class XI Chapter 9 - Sequences and

- Page 289 and 290:
Class XI Chapter 9 - Sequences and

- Page 291 and 292:
Class XI Chapter 9 - Sequences and

- Page 293 and 294:
Class XI Chapter 9 - Sequences and

- Page 295 and 296:
Class XI Chapter 9 - Sequences and

- Page 297 and 298:
Class XI Chapter 9 - Sequences and

- Page 299 and 300:
Class XI Chapter 9 - Sequences and

- Page 301 and 302:
Class XI Chapter 9 - Sequences and

- Page 303 and 304:
Class XI Chapter 9 - Sequences and

- Page 305 and 306:
Class XI Chapter 9 - Sequences and

- Page 307 and 308:
Class XI Chapter 9 - Sequences and

- Page 309 and 310:
Class XI Chapter 9 - Sequences and

- Page 311 and 312:
Class XI Chapter 9 - Sequences and

- Page 313 and 314:
Class XI Chapter 10 - Straight Line

- Page 315 and 316:
Class XI Chapter 10 - Straight Line

- Page 317 and 318:
Class XI Chapter 10 - Straight Line

- Page 319 and 320:
Class XI Chapter 10 - Straight Line

- Page 321 and 322:
Class XI Chapter 10 - Straight Line

- Page 323 and 324:
Class XI Chapter 10 - Straight Line

- Page 325 and 326:
Class XI Chapter 10 - Straight Line

- Page 327 and 328:
Class XI Chapter 10 - Straight Line

- Page 329 and 330:
Class XI Chapter 10 - Straight Line

- Page 331 and 332:
Class XI Chapter 10 - Straight Line

- Page 333 and 334:
Class XI Chapter 10 - Straight Line

- Page 335 and 336:
Class XI Chapter 10 - Straight Line

- Page 337 and 338:
Class XI Chapter 10 - Straight Line

- Page 339 and 340:
Class XI Chapter 10 - Straight Line

- Page 341 and 342:
Class XI Chapter 10 - Straight Line

- Page 343 and 344:
Class XI Chapter 10 - Straight Line

- Page 345 and 346:
Class XI Chapter 10 - Straight Line

- Page 347 and 348:
Class XI Chapter 10 - Straight Line

- Page 349 and 350:
Class XI Chapter 10 - Straight Line

- Page 351 and 352:
Class XI Chapter 10 - Straight Line

- Page 353 and 354:
Class XI Chapter 10 - Straight Line

- Page 355 and 356:
Class XI Chapter 10 - Straight Line

- Page 357 and 358:
Class XI Chapter 10 - Straight Line

- Page 359 and 360:
Class XI Chapter 10 - Straight Line

- Page 361 and 362:
Class XI Chapter 10 - Straight Line

- Page 363 and 364:
Class XI Chapter 10 - Straight Line

- Page 365 and 366:
Class XI Chapter 10 - Straight Line

- Page 367 and 368:
Class XI Chapter 10 - Straight Line

- Page 369 and 370:
Class XI Chapter 10 - Straight Line

- Page 371 and 372:
Class XI Chapter 10 - Straight Line

- Page 373 and 374:
Class XI Chapter 11 - Conic Section

- Page 375 and 376:
Class XI Chapter 11 - Conic Section

- Page 377 and 378:
Class XI Chapter 11 - Conic Section

- Page 379 and 380:
Class XI Chapter 11 - Conic Section

- Page 381 and 382:
Class XI Chapter 11 - Conic Section

- Page 383 and 384:
Class XI Chapter 11 - Conic Section

- Page 385 and 386:
Class XI Chapter 11 - Conic Section

- Page 387 and 388:
Class XI Chapter 11 - Conic Section

- Page 389 and 390:
Class XI Chapter 11 - Conic Section

- Page 391 and 392:
Class XI Chapter 11 - Conic Section

- Page 393 and 394:
Class XI Chapter 11 - Conic Section

- Page 395 and 396:
Class XI Chapter 11 - Conic Section

- Page 397 and 398:
Class XI Chapter 11 - Conic Section

- Page 399 and 400:
Class XI Chapter 11 - Conic Section

- Page 401 and 402:
Class XI Chapter 11 - Conic Section

- Page 403 and 404:
Class XI Chapter 11 - Conic Section

- Page 405 and 406:
Class XI Chapter 11 - Conic Section

- Page 407 and 408:
Class XI Chapter 11 - Conic Section

- Page 409 and 410:
Class XI Chapter 11 - Conic Section

- Page 411 and 412:
Class XI Chapter 11 - Conic Section

- Page 413 and 414:
Class XI Chapter 11 - Conic Section

- Page 415 and 416:
Class XI Chapter 11 - Conic Section

- Page 417 and 418:
Class XI Chapter 12 - Introduction

- Page 419 and 420:
Class XI Chapter 12 - Introduction

- Page 421 and 422:
Class XI Chapter 12 - Introduction

- Page 423 and 424:
Class XI Chapter 12 - Introduction

- Page 425 and 426:
Class XI Chapter 12 - Introduction

- Page 427 and 428:
Class XI Chapter 12 - Introduction

- Page 429 and 430:
Class XI Chapter 12 - Introduction

- Page 431 and 432:
Class XI Chapter 13 - Limits and De

- Page 433 and 434:
Class XI Chapter 13 - Limits and De

- Page 435 and 436:
Class XI Chapter 13 - Limits and De

- Page 437 and 438:
Class XI Chapter 13 - Limits and De

- Page 439 and 440:
Class XI Chapter 13 - Limits and De

- Page 441 and 442:
Class XI Chapter 13 - Limits and De

- Page 443 and 444:
Class XI Chapter 13 - Limits and De

- Page 445 and 446:
Class XI Chapter 13 - Limits and De

- Page 447 and 448:
Class XI Chapter 13 - Limits and De

- Page 449 and 450:
Class XI Chapter 13 - Limits and De

- Page 451 and 452:
Class XI Chapter 13 - Limits and De

- Page 453 and 454:
Class XI Chapter 13 - Limits and De

- Page 455 and 456:
Class XI Chapter 13 - Limits and De

- Page 457 and 458:
Class XI Chapter 13 - Limits and De

- Page 459 and 460:
Class XI Chapter 13 - Limits and De

- Page 461 and 462:
Class XI Chapter 13 - Limits and De

- Page 463 and 464:
Class XI Chapter 13 - Limits and De

- Page 465 and 466:
Class XI Chapter 13 - Limits and De

- Page 467 and 468:
Class XI Chapter 13 - Limits and De

- Page 469 and 470:
Class XI Chapter 13 - Limits and De

- Page 471 and 472:
Class XI Chapter 13 - Limits and De

- Page 473 and 474:
Class XI Chapter 13 - Limits and De

- Page 475 and 476:
Class XI Chapter 13 - Limits and De

- Page 477 and 478:
Class XI Chapter 13 - Limits and De

- Page 479 and 480:
Class XI Chapter 13 - Limits and De

- Page 481 and 482:
Class XI Chapter 13 - Limits and De

- Page 483 and 484:
Class XI Chapter 13 - Limits and De

- Page 485 and 486:
Class XI Chapter 13 - Limits and De

- Page 487 and 488:
Class XI Chapter 13 - Limits and De

- Page 489 and 490:
Class XI Chapter 13 - Limits and De

- Page 491 and 492:
Class XI Chapter 14 - Mathematical

- Page 493 and 494:
Class XI Chapter 14 - Mathematical

- Page 495 and 496:
Class XI Chapter 14 - Mathematical

- Page 497 and 498:
Class XI Chapter 14 - Mathematical

- Page 499 and 500:
Class XI Chapter 14 - Mathematical

- Page 501 and 502:
Class XI Chapter 14 - Mathematical

- Page 503 and 504:
Class XI Chapter 14 - Mathematical

- Page 505 and 506:
Class XI Chapter 14 - Mathematical

- Page 507 and 508:
Class XI Chapter 15 - Statistics Ma

- Page 509 and 510:
Class XI Chapter 15 - Statistics Ma

- Page 511 and 512:
Class XI Chapter 15 - Statistics Ma

- Page 513 and 514:
Class XI Chapter 15 - Statistics Ma

- Page 515 and 516:
Class XI Chapter 15 - Statistics Ma

- Page 517 and 518:
Class XI Chapter 15 - Statistics Ma

- Page 519 and 520:
Class XI Chapter 15 - Statistics Ma

- Page 521 and 522:
Class XI Chapter 15 - Statistics Ma

- Page 523 and 524:
Class XI Chapter 15 - Statistics Ma

- Page 525 and 526:
Class XI Chapter 15 - Statistics Ma

- Page 527 and 528:
Class XI Chapter 15 - Statistics Ma

- Page 529 and 530:
Class XI Chapter 15 - Statistics Ma

- Page 531 and 532:
Class XI Chapter 15 - Statistics Ma

- Page 533 and 534:
Class XI Chapter 15 - Statistics Ma

- Page 535:
Class XI Chapter 15 - Statistics Ma