170321
AssignmentMultiple Select

Powers and Roots of Complex Numbers

Question 170321 • Precalculus

Determine which regions contain cube roots of −1. Check all that apply.on real axison imaginary axisquadrant 1quadrant 2quadrant 3quadrant 4

Answer
A
on real axis
B
on imaginary axis
C
quadrant 1
D
quadrant 2
E
quadrant 3
F
quadrant 4

Explanation

Write −1 as a complex number with angle π. Its cube roots have angles (π + 2πk)/3 for k = 0, 1, 2, giving π/3, π, and 5π/3. These lie in quadrant 1, on the real axis, and in quadrant 4, respectively.

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