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  4. If ((1+i/1-i))x =1, then

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Q. If $\left(\frac{1+i}{1-i}\right)^{x} =1$, then

Complex Numbers and Quadratic Equations

Solution:

$\left(\frac{1+i}{1-i}\right)^{x} =1$
$\Rightarrow \left(\frac{1+i}{1-i}\times\frac{1+i}{1+i}\right)^{x}=1$
$\Rightarrow \left(i\right)^{x}=1$
For $x = 4n$,
$i^{x}=1$