Purely imaginary number
Purely imaginary number
IB Year 6 | Grade 12
If \(|z|=1\) and \(z\ne-1\), prove that the complex number \(\frac{z-1}{z+1}\) has zero real part.
Solution:
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Answer:\(\operatorname{Re}\left(\frac{z-1}{z+1}\right)=0\); the quotient is zero at \(z=1\).
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