6. Let z E C. Let C be set of points z satisfying Im(z) 0 and Im Prove that C = {ZEC : |Z| = 1}. Hint: If Im(z) = 0 then Im() = 0. 1+z+z² 1-z+z² = 0.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 23E
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6. Let z E C. Let C be set of points z satisfying
Im(z) 0 and Im
Im (1+²+2²)
Prove that C = {ZEC : |Z| = 1}.
Hint: If Im(z) = 0 then Im() = 0.
= 0.
Transcribed Image Text:6. Let z E C. Let C be set of points z satisfying Im(z) 0 and Im Im (1+²+2²) Prove that C = {ZEC : |Z| = 1}. Hint: If Im(z) = 0 then Im() = 0. = 0.
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