6
QuizMultiple Choice

Powers and Roots of Complex Numbers

Question 6 • Precalculus

Where are the 4th roots of 16i located?

Answer
A
on a circle with radius 1.7
B
on a circle with radius 2
C
on a circle with radius 2.5
D
on a circle with radius 4

Explanation

If z is a fourth root of 16i, then z⁴ = 16i, so |z|⁴ = |16i| = 16. Thus |z| = 16^(1/4) = 2. All four roots lie on a circle centered at the origin with radius 2, so the correct choice is “on a circle with radius 2.”

AI-written and checked against the verified answer.

Previous
Next