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If z is any complex number satisfying |z - 1| = 1, then which is following is correct ?

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If z is any complex number satisfying |z - 1| = 1, then which is following is correct ? 

(1) arg(z-1)=2argz

(2) arg(z-1)=arg(z+1) 

(3) argz = 2 arg (z+1) 

(4) 2 arg (z) = 2/3 arg(z2 - z)

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1 Answer

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Best answer

Correct option is (1) arg(z - 1) = 2argz 

Put z = cos θ + i sinθ

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