Question

if arg(z-1/z+1)=π/2,the prove that |z|=1​

Answer 1

Step-by-step explanation:

arg(

z+1

z−1

)=

2

π

implies

angle between the complex numbers

z−1 and z+1 is

2

π

in complex plane.

Clearly, as angle subtended by a diametric at point on circle is 90

0

⇒ Here -1 and 1 are end-points of a diameter.

⇒ diameter =∣1−(−1)∣=2

radius =1 unit

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