Let (zn)n≥1 be a geometric progression of complex numbers, and suppose that z3 = −1 and z5 = 7. Find all possible values of z2. Please Note. You should leave any square roots that arise in your answer.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 60E
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 Let (zn)n≥1 be a geometric progression of complex numbers, and suppose that z3 = −1 and z5 = 7. Find all possible values of z2.
Please Note. You should leave any square roots that arise in your answer. 

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