Cool Complex! #02

Algebra Level 4

If |z| = 1 and ω = z − 1 z + 1 \omega = \frac {z-1}{z+1} ( z ≠ − 1 ) (z\neq -1) , then R e ( ω ) Re(\omega) is

Source : IIT JEE, 2003


The answer is 0.

Saurav Pal by Saurav Pal , 26, India

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1 solution

It is not reduced generalization to assume that: z = i ; ⇒ ϖ = 1 − i 1 + i = − 2 i 2 = − i z=i; \Rightarrow \varpi=\frac{1-i}{1+i}=\frac{-2i}{2}=-i R e ( ϖ ) = 0 Re(\varpi)=\boxed{0}

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Nice objective approach!, but can you give a subjective method to solve this?

Saurav Pal - 6 years, 3 months ago

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