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  4. If (1-i α/1+i α)=A +i B, then A2+B2 equals to

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Q. If $\frac{1-i \alpha}{1+i \alpha}=A +i B$, then $A^{2}+B^{2}$ equals to

BITSATBITSAT 2010

Solution:

$A+i B=\frac{1-i \alpha}{1+i \alpha}$
$\Rightarrow A=i B=\frac{1+i \alpha}{1-i \alpha}$
$\Rightarrow (A+i B)(A-i B)$
$=\frac{(1-i \alpha)(1+i \alpha)}{(1+i \alpha)(1-i \alpha)}=1$
$\Rightarrow A^{2}+B^{2}=1$