Multiply and Divide Complex Numbers

Question 1

What is the product of 16(cos(47°) + i sin(47°)) and 4(cos(12°) + i sin(12°))?

Revolt · Accepted Answer

64(cos(59°) + i sin(59°))

Question 2

Let z = 0.3(cos(31°) + i sin(31°)) and w = 20(cos(18°) + i sin(18°)).Which statement describes the geometric construction of the product zw on the complex plane?

Revolt · Accepted Answer

Stretch z by a factor of 20, then rotate 18° counterclockwise.

Question 3

For z = –3 – 5i, which graph shows z and the product of z · i?

Revolt · Accepted Answer

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is (negative 3, negative 5) and point z times I is (5, negative 3).

Question 4

Let z = 5 – 9i and w = 6 + i. Which expression shows the first step in finding the quotient of ?

Revolt · Accepted Answer

StartFraction 5 minus 9 I Over 6 + I EndFraction times StartFraction 6 minus I Over 6 minus I EndFraction

Question 5

Review the graphs of complex numbers z and w.

Revolt · Accepted Answer

8 + 2i

Question 6

Let z = and .What is zw?

Revolt · Accepted Answer

77 (cosine (StartFraction pi Over 6 EndFraction) + I sine (StartFraction pi Over 6 EndFraction))

Question 7

Which statement describes how to geometrically determine the product of z = 25 – i and w = + 3i on the complex plane?

Revolt · Accepted Answer

Stretch z by a factor of and rotate 60° counterclockwise.

Question 8

Which statement describes how to geometrically divide a complex number, z, by a second complex number, w?

Revolt · Accepted Answer

Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

Question 9

What is the product of (3 + 5i) and (2 – 6i)?

Revolt · Accepted Answer

36 – 8i

Question 10

For the complex numbers z = and , which geometric transformation of z on the complex plane describes the quotient ?

Revolt · Accepted Answer

Scale z by a factor of , then rotate clockwise by radians.

Multiply and Divide Complex Numbers Answers

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