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Question

If |z|=1 , then arg((1+z)(1z)) will be

A
π6 or 5π6
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B
π3 or 2π3
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C
π4 or 3π4
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D
π2,π
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Solution

The correct option is C π4 or 3π4

Since |z|=1,z lies on a unit circle having centre at the origin
Form the above diagram
arg(1+z1z)=π2 or 3π2
1+z1z=keiπ/2 or kei3π/2
where k is a real parameter and its value depends upon the position of z.
arg((1+z)(1z))=π4 or 3π4

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