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If (z 1 -2z 2 /2-z 1 z 2 ) is unimodulus and z 2 is not unimodulus then find | z 1 |?

If (z1 -2z2  /2-z1 z2 ) is unimodulus and  z2  is not unimodulus then find | z1 |?

Grade:12

3 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

Given:
|\frac{z_{1}-2z_{2}}{1-2z_{1}z_{2}}| = 1
|z_{1}-2z_{2}| =|1-2z_{1}z_{2}|
|z_{1}-2z_{2}|^{2} =|1-2z_{1}z_{2}|^{2}
|z_{1}|^{2}+4|z_{2}|^{2}-4|z_{1}||z_{2}| = 1 + 4|z_{1}|^{2}|z_{2}|^{2} - 4|z_{1}||z_{2}|
|z_{1}|^{2}+4|z_{2}|^{2} = 1 + 4|z_{1}|^{2}|z_{2}|^{2}
|z_{1}|^{2}(1-4|z_{2}|^{2}) = 1-4|z_{2}|^{2}
|z_{1}|^{2} = 1
|z_{1}| = 1


mycroft holmes
272 Points
7 years ago
Testing Latex 
mycroft holmes
272 Points
7 years ago
By the way you cannot expand the modulus squared the way you have done. Please revise your answer

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