Find the product and write the result in standard form.

QUESTION 1 Write the complex number in standard form 3(cos 225° + i sin 225°).

A.

B.

C.

D.

E. QUESTION 2 Find the product and write the result in standard form. (2 – 6i)2

A. -32

B. 4 – 24i + 36i2

C. 40 – 24i

D. -32 – 24i

QUESTION 3 Perform the indicated operation.(2 – 5i) + (8 + 7i)

A. 10 – 2i

B. 10 + 2i

C. -10 – 2i

D. -6 + 12i

QUESTION 4 Use DeMoivre’s Theorem to find the indicated power of the complex number. [2(cos 15° + i sin 15°)]4

A.

B. 8 + 8i

C.

D. 16i

QUESTION 5 Find the quotient (z1/z2) of the complex numbers. z1 = 5(cos 200° + i sin 200°) z2 = 4(cos 50° + i sin 50°)

A. (5/4)(cos 150° – i sin 150°)

B. (5/4)(cos 150° + i sin 150°)

C. (5/4)(sin 150° + i cos 150°)

D. (5/4)(cos 250° + i sin 250°)

QUESTION 6 Find the product and write the result in standard form. -2i(7i – 4)

A. -14 + 8i

B. 8i – 14i2

C. 14 + 8i

D. 8i + 14i2

QUESTION 7 Perform the indicated operation.(4 + 5i) – (-7 + i)

A. -3 + 6i

B. 11 + 4i

C. -11 – 4i

D. 11 – 4i

QUESTION 8 Write the complex number 6i in trigonometric form.

A. 6(cos 180° + i sin 180°)

B. 6(cos 270° + i sin 270°)

C. 6(cos 0° + i sin 0°)

D. 6(cos 90° + i sin 90°)

QUESTION 9 Find the absolute value of the complex number. z = -7

A. 0

B. -7

C. 7

D. 14

QUESTION 10

A.

B.

C.

D.

QUESTION 11 Find the complex square roots of 49(cos 30° + i sin 30°)

A. 7(cos 30° + i sin 30°), -7(cos 105° + i sin 105°)

B. 7(cos 15° + i sin 15°), 105(cos 195° + i sin 195°)

C. 7(cos 15° + i sin 15°), 7(cos 195° + i sin 195°)

D. 7(cos 30° + i sin 30°), 7(cos 105° + i sin 105°)

QUESTION 12 Write the complex number 6 + 8i in trigonometric form.

A. 10(cos 53.1° + i sin 53.1°)

B. 10(cos 306.9° + i sin 306.9°)

C. 10(cos 233.1° + i sin 233.1°)

D. 10(cos 126.9° + i sin 126.9°)

QUESTION 13 Find the absolute value of the complex number z = -11 – 6i

A.

B.

C.

D.

QUESTION 14 1. Find the product of the complex numbers.z1 = 5(cos 20° + i sin 20°)z2 = 4(cos 10° + i sin 10°)

A. 9(cos 30° + i sin 30°)

B. 20(cos 10° + i sin 10°)

C. 20(cos 30° + i sin 30°)

D. 9(-cos 200° – i sin 200°)

QUESTION 15 Find the complex cube roots of 343(cos 291° + i sin 291°)

A. -7(cos 97° + i sin 97°), 7(cos 217° + i sin 217°), -7(cos 337° + i sin 337°)

B. 7(cos 97° – i sin 97°), 7(cos217° – i sin 217°), 7(cos 337° – i sin 337°)

C. 7(cos 97° + i sin 97°), 7(cos217° + i sin 217°), 7(cos 337° + i sin 337°)

D. -7(cos 97° + i sin 97°), 7(cos 137° + i sin 137°), -7(cos 177° + i sin 177°)

E. 7(cos 97° + i sin 97°), 7(cos 137° + i sin 137°), 7(cos 177° + i sin 177°)

QUESTION 16 Find the product and write the result in standard form (4 + 5i)(2 – 8i)

A. 48 + 22i

B. 40i2 – 22i + 8

C. 48 – 22i

D. -32 + 42i

QUESTION 17 Find the product of the complex numbers.z1 = 7(cos (π/4) + i sin (π /4))z2 = 3(cos (π /6) + i sin (π /6))

A. 10(cos (π/12) + i sin (π/12))

B. 21(cos (π/12) + i sin (π/12))

C. 10(cos (5π /12) + i sin (5π /12))

D. 21(cos (5 π/12) + i sin (5 π/12))

QUESTION 18 Perform the indicated operation.5i – (-5 – i)

A. -5 + 4i

B. 5 + 6i

C. 5 – 4i

D. -5 – 6i

QUESTION 19 Find the absolute value of the complex number z = -8 – 12i

A. 2

B. 2i√13

C. 4√13

D. 4i√13

QUESTION 20 Use DeMoivre’s Theorem to find the indicated power of the complex number. (1 – i)10

A. 32 – 32i

B. 32

C. -32i

D. -32 + 32i


 

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