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Hello sir /madam please solve the above property i am not understaning .kindly please solve the question thankyou.

Hello sir /madam please solve the above property i am not understaning .kindly please solve the question thankyou.

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Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
5 years ago
|z1 – z2|=|z1 + z2|
divide by |z2| on both sides
|z1/z2–1|=|z1/z2+1|
let z1/z2=z
so |z-1|=|z+1|
but |z-1| and |z+1| represent the distance of z from 1 and -1 respectively. for both these distances to be equal, z must lie on the perpendicular bisector of the line joining 1 and –1, which happens to be the imaginary axis. hence z lies on the imaginary axis and hence z=z1/z2 is purely imaginary.
this means that argz=+-pi/2
arg(z1/z2)=+-pi/2
or arg(z1) – arg(z2)=+-pi/2

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