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Grade 12Algebra

If (z₁-2z₂/2-z₁z₂) is unimodulus and z₂ is not unimodulus then find | z₁|?

harendar singh

16 Years agoGrade 12

3 Answers

Jitender Singh

11 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

11 Years ago

Testing Latex $\sqrt2$

mycroft holmes

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

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