If `((z-1)/(z+1))` is purely an imaginary number and `z ne -1` then fi – InterviewSolution

InterviewSolution

1.	If `((z-1)/(z+1))` is purely an imaginary number and `z ne -1` then find the value of \|z\|.
Answer» Correct Answer - \|z\| = 1 Let z = x + iy. Then, `(z-1)/(z+1)=((x-1)+iy)/((x+1)+iy)xx((x+1)-iy)/((x+1)-iy)=((x^(2)+y^(2)-1)+(x+y)i)/((x+1)^(2)+y^(2))` Now, `(z-1)/(z+1)` is purely imaginary `iff x^(2) + y^(2) -1 = 0 iff x^(2) + y^(2) = 1 iff \|z\| = 1`.

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