Question
If x + iy = $\frac{a+i b}{a-i b}$, prove that x2 + y2 = 1
Squaring Both the sides,
=> |x + iy|2 =$\frac{|(a+i b)|^2}{|(a-i b)|^2}$
=> x2 + y2 = $\frac {a^2 + b^2} {a^2 + b^2}$ = 1
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$\frac{\text{a}}{1+\text{i}}+\frac{\text{a}}{(1+\text{i})^2}+\frac{\text{a}}{(1+\text{i})^3}+\ ...\ +\frac{\text{a}}{(1+\text{i})^\text{n}}.$