1 Foundations 2 Solving Linear Equations 3 Graphs And Functions 4 Systems Of Linear Equations 5 Polynomials And Polynomial Functions 6 Factoring 7 Rational Expressions And Functions 8 Roots And Radicals 9 Quadratic Equations And Functions 10 Exponential And Logarithmic Functions 11 Conics 12 Sequences, Series And Binomial Theorem Chapter8: Roots And Radicals
8.1 Simplify Expressions With Roots 8.2 Simplify Radical Expressions 8.3 Simplify Rational Exponents 8.4 Add, Subtract, And Multiply Radical Expressions 8.5 Divide Radical Expressions 8.6 Solve Radical Equations 8.7 Use Radicals In Functions 8.8 Use The Complex Number System Chapter Questions Section8.8: Use The Complex Number System
Problem 8.151TI: Write each expression in terms of i and simplify if possible: (a) 81 (b) 5 (c) 18. Problem 8.152TI: Write each expression in term of i and simplify if possible: (a) 36 (b) 3 (c) 27. Problem 8.153TI: Add: 8+32. Problem 8.154TI: Add: 27+48. Problem 8.155TI: Simplify: (a) (2+7i)+(42i) (b) (84i)(2i). Problem 8.156TI: Simplify: (a) (32i)+(54i) (b) (4+3i)(26i). Problem 8.157TI: Multiply: 4i(53i). Problem 8.158TI: Multiply: 3i(2+4i). Problem 8.159TI: Multiply: (53i)(12i) Problem 8.160TI: Multiply: (43i)(2+i) Problem 8.161TI: Multiply using the Binomial Squares pattern: (25i)2. Problem 8.162TI: Multiply using the Binomial Squares pattern: (5+4i)2. Problem 8.163TI: Multiply: 494. Problem 8.164TI: Multiply: 3681. Problem 8.165TI: Multiply: (412)(348). Problem 8.166TI: Multiply: (2+8)(318). Problem 8.167TI: Multiply: (43i)(4+3i). Problem 8.168TI: Multiply: (2+5i)(25i). Problem 8.169TI: Multiply using the Product of Complex Conjugates Pattern: (310i)(3+10i). Problem 8.170TI: Multiply using the Product of Complex Conjugates Pattern: (5+4i)(54i). Problem 8.171TI: Divide: 2+5i52i. Problem 8.172TI: Divide: 1+6i6i. Problem 8.173TI: Divide, writing the answer in standard form: 414i. Problem 8.174TI: Divide writing the answer in standard form: 21+2i. Problem 8.175TI: Divide: 3+3i2i. Problem 8.176TI: Divide: 2+4i5i. Problem 8.177TI: Simplify: i75. Problem 8.178TI: Simplify: i92. Problem 409E: In the following exercises, write each expression in terms of i and simplify if possible. 409. (a)... Problem 410E: In the following exercises, write each expression in terms of i and simplify if possible. 410. (a)... Problem 411E: In the following exercises, write each expression in terms of i and simplify if possible. 411. (a)... Problem 412E: In the following exercises, write each expression in terms of i and simplify if possible. 412. (a)... Problem 413E: In the following exercises, add or subtract. 413. 75+48 Problem 414E: In the following exercises, add or subtract. 414. 12+75 Problem 415E: In the following exercises, add or subtract. 415. 50+18 Problem 416E: In the following exercises, add or subtract. 416. 72+8 Problem 417E: In the following exercises, add or subtract. 417. (1+3i)+(7+4i) Problem 418E: In the following exercises, add or subtract. 418. (6+2i)+(34i) Problem 419E: In the following exercises, add or subtract. 419. (8i)+(6+3i) Problem 420E: In the following exercises, add or subtract. 420. (74i)+(26i) Problem 421E: In the following exercises, add or subtract. 421. (14i)(36i) Problem 422E: In the following exercises, add or subtract. 422. (84i)(3+7i) Problem 423E: In the following exercises, add or subtract. 423. (6+i)(24i) Problem 424E: In the following exercises, add or subtract. 424. (2+5i)(5+6i) Problem 425E: In the following exercises, add or subtract. 425. (536)+(249) Problem 426E: In the following exercises, add or subtract. 426. (3+64)+(516) Problem 427E: In the following exercises, add or subtract. 427. (750)(3018) Problem 428E: In the following exercises, add or subtract. 428. (5+27)(448) Problem 429E: In the following exercises, multiply. 429. 4i(53i) Problem 430E: In the following exercises, multiply. 430. 2i(3+4i) Problem 431E: In the following exercises, multiply. 431. 6i(32i) Problem 432E: In the following exercises, multiply. 432. i(6+5i) Problem 433E: In the following exercises, multiply. 433. (4+3i)(5+6i) Problem 434E: In the following exercises, multiply. 434. (25i)(4+3i) Problem 435E: In the following exercises, multiply. 435. (3+3i)(27i) Problem 436E: In the following exercises, multiply. 436. (62i)(35i) Problem 437E: In the following exercises, multiply using the Product of Binomial Squares Pattern. 437. (3+4i)2 Problem 438E: In the following exercises, multiply using the Product of Binomial Squares Pattern. 438. (1+5i)2 Problem 439E: In the following exercises, multiply using the Product of Binomial Squares Pattern. 439. (23i)2 Problem 440E: In the following exercises, multiply using the Product of Binomial Squares Pattern. 440. (65i)2 Problem 441E: In the following exercises, multiply. 441. 2536 Problem 442E: In the following exercises, multiply. 442. 416 Problem 443E: In the following exercises, multiply. 443. 9100 Problem 444E: In the following exercises, multiply. 444. 649 Problem 445E: In the following exercises, multiply. 445. (227)(448) Problem 446E: In the following exercises, multiply. 446. (512)(3+75) Problem 447E: In the following exercises, multiply. 447. (2+8)(4+18) Problem 448E: In the following exercises, multiply. 448. (5+18)(250) Problem 449E: In the following exercises, multiply. 449. (2i)(2+i) Problem 450E: In the following exercises, multiply. 450. (45i)(4+5i) Problem 451E: In the following exercises, multiply. 451. (72i)(7+2i) Problem 452E: In the following exercises, multiply. 452. (38i)(3+8i) Problem 453E: In the following exercises, multiply using the Product of Complex Conjugates Pattern. 453. (7i)(7+i) Problem 454E: In the following exercises, multiply using the Product of Complex Conjugates Pattern. 454.... Problem 455E: In the following exercises, multiply using the Product of Complex Conjugates Pattern. 455.... Problem 456E: In the following exercises, multiply using the Product of Complex Conjugates Pattern. 456.... Problem 457E: In the following exercises, divide. 457. 3+4i43i Problem 458E: In the following exercises, divide. 458. 52i2+5i Problem 459E: In the following exercises, divide. 459. 2+i34i Problem 460E: In the following exercises, divide. 460. 32i6+i Problem 461E: In the following exercises, divide. 461. 323i Problem 462E: In the following exercises, divide. 462. 245i Problem 463E: In the following exercises, divide. 463. 432i Problem 464E: In the following exercises, divide. 464. 13+2i Problem 465E: In the following exercises, divide. 465. 1+4i3i Problem 466E: In the following exercises, divide. 466. 4+3i7i Problem 467E: In the following exercises, divide. 467. 23i4i Problem 468E: In the following exercises, divide. 468. 35i2i Problem 469E: In the following exercises, simplify. 469. i41 Problem 470E: In the following exercises, simplify. 470. i39 Problem 471E: In the following exercises, simplify. 471. i66 Problem 472E: In the following exercises, simplify. 472. i48 Problem 473E: In the following exercises, simplify. 473. i128 Problem 474E: In the following exercises, simplify. 474. i162 Problem 475E: In the following exercises, simplify. 475. i137 Problem 476E: In the following exercises, simplify. 476. i255 Problem 477E: Explain the relationship between real numbers and complex numbers. Problem 478E: Aniket multiplied as follows and he got the wrong answer. What is wrong with his reasoning? 77497 Problem 479E: Why is 64=8i but 643=4. Problem 480E: Explain how dividing complex numbers is similar to rationalizing a denominator. Problem 8.167TI: Multiply: (43i)(4+3i).
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Select the basic integration formula you can use to find the indefinite integral, and identify u and a when appropriate. Do not integrate.
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dx
xVx² – 4
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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