lf `z(!=-1)` is a complex number such that `[z-1]/[z+1]` is purely ima – InterviewSolution

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1.	lf `z(!=-1)` is a complex number such that `[z-1]/[z+1]` is purely imaginary, then `\|z\|` is equal to
Answer» Let z = (x + iy). Then, `(z-1)/(z+1)=((x+iy)-1)/((x+iy)+1)=((x-1)+iy)/((x+1)+iy)xx((x+1)-iy)/((x+1)-iy)=((x^(2)+y^(2)-1)+2iy)/((x+1)^(2)+y^(2))` `(z-1)/(z+1)` is purely imaginary `iff x^(2) - 1 = 0 iff x^(2) + y^(2) = 1 iff \|z\| = 1`.

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