Test — Test Answers

Review the graph.

Which region on the unit circle contains a cube root of – 8 – 8i?

Review the proof of de Moivre’s theorem. 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) + i sin(kθ)] ∙ [cos(θ) + i sin(θ)]C= cos(kθ)cos(θ) − sin(kθ)sin(θ) + i [sin(kθ)cos(θ) + cos(kθ) sin(θ)]D= cos(kθ + θ) + i sin(kθ + θ)E= cos[(k + 1)θ] + i sin[(k + 1)θ]

If z = 1 + i, what is z5?

Which number represents the sum of –8 and –i?

What is the quotient of ?

Let z = 19 + i and w = 4 + 10i.What is the first step in determining zw?

Consider z = 3 + 3i. What happens to the modulus and argument when z is raised to the 4th power?

Which phrase describes how to divide a complex number z by r(cos θ + i sin θ)?

For two complex numbers z and w, which diagram shows the geometric representation of zw?

Given z1 = 2 + and z2 = 1 – , what is the sum of z1 and z2?