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If |ω|=1 , then the set of points z=ω+1ω is satisfies

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a

|Re⁡(z)|≤2

b

|z|≤1

c

|z|=1

d

|Im⁡(z)|≥2

answer is A.

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Detailed Solution

As |ω|=1⇒|ω|2=1⇒ωω¯=1⇒1ω=ω¯Thus, z=ω+1/ω=ω+ω¯=2Re⁡(ω)Now, |Re⁡(z)|=|2Re⁡(ω)|=|2Re⁡(ω)|≤2|ω|=2

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