If $(x+i y)=\left(\frac{1+i}{1-i}\right)^3-\left(\frac{1-i}{1+i}\right)^3$, then the true statement among the following is

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Aicharya · Accepted Answer

Given $(\mathrm{x}+\mathrm{iy})=\left(\frac{1+\mathrm{i}}{1-\mathrm{i}}ight)^3-\left(\frac{1-\mathrm{i}}{1+\mathrm{i}}ight)^3$ $ \begin{aligned} & \Rightarrow x-i y=\left\{\left(\frac{1+i}{1-i} 	imes \frac{1+i}{1+i}ight)-\left(\frac{1-i}{1+i} 	imes \frac{1-i}{1+i}ight)ight\} \ & =\frac{1}{8}[-8 i-8 i] \ & =-2 i \ & x+i y=0+(-2) i \ & \Rightarrow x>y \end{aligned} $

If $(x+i y)=\left(\frac{1+i}{1-i}\right)^3-\left(\frac{1-i}{1+i}\right)^3$, then the true statement among…

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