Powers and Roots of Complex Numbers — Unit test

Question 1

Let z = and .Which statement describes the geometric construction of the product zw on the complex plane?

Revolt · Accepted Answer

Stretch z by a factor of 3 and rotate radians counterclockwise.

Question 2

A circle has a diameter with endpoints at –2 + i and –6 –11i. What is the center of the circle?

Revolt · Accepted Answer

–4 – 5i

Question 3

Let z = 9 – 2i and zw = 25 + 70i.What is w?

Revolt · Accepted Answer

1 + 8i

Question 4

What is the modulus of 6 + 7i?

Revolt · Accepted Answer

root 85

Question 5

Review the proof of de Moivre’s theorem (not in order). Proof of de Moivre's Theorem [cos(θ) + i sin(θ)]k + 1A= [cos(θ) + i sin(θ)]k ∙ [cos(θ) + i sin(θ)]1B= cos(kθ + θ) + i sin(kθ + θ)C= cos(kθ)cos(θ) − sin(kθ)sin(θ) + i [sin(kθ)cos(θ) + cos(kθ)sin(θ)]D= [cos(kθ) + i sin(kθ)] ∙ [cos(θ) + i sin(θ)]E= cos[(k + 1)θ] + i sin[(k + 1)θ]

Revolt · Accepted Answer

steps B and D

Powers and Roots of Complex Numbers — Unit test Answers

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