Powers and Roots of Complex Numbers Answers

Where are the 4th roots of 16i located?

What is the modulus after (–1 + ) gets raised to the 6th power?

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= ?E= cos[(k + 1)θ] + i sin[(k + 1)θ]

What is the distance on the unit circle between successive fourth roots of ?

Which expression is equivalent to ?

Review the graph.

Which of the following is a square root of ?

If z = 1 – i, what is z3?

Which expression represents a cube root of 1 + i?

Suppose z = . What is z4?