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

harendar singh , 14 Years ago

Grade 12

3 Answers

Jitender Singh

Last Activity: 10 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

Last Activity: 10 Years ago

Testing Latex $\sqrt2$

mycroft holmes

Last Activity: 10 Years ago

By the way you cannot expand the modulus squared the way you have done. Please revise your answer

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