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if (z-2)/(z+2) is purely imaginary then find the value of |z| ?

if (z-2)/(z+2) is purely imaginary
then find the value of
|z|   ?

Grade:11

2 Answers

Abhishek Singh
93 Points
6 years ago
if a complex no. is purely img. then its real part must be zero.
using the relation
for any  z+(conj z)= 2real part of Z
using this and solving you will get mod(z)=2
Akshay bansal
11 Points
3 years ago
z-2/z+2 =[(x-2)+yi]/[x+2+ yi] × (x+2)-yi/(x+2-yi=>|z|^2-4/|z|^2+4+4x =0. (since x^2+ y^2=|z|^2 and the entire rain is imaginary so real=0)=>|z|^2-4=0=>|z|=2

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