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Question: If \(\frac{1 - i\alpha}{1 + i\alpha}\) = A + iB, then A<sup>2</sup> + B<sup>2</sup> equals –...

If 1−iα1+iα\frac{1 - i\alpha}{1 + i\alpha} = A + iB, then A2 + B2 equals –

A

1

B

a2

C

–1

D

–a2

Answer

1

Explanation

Solution

Sol. A + iB = 1−iα1+iα\frac{1 - i\alpha}{1 + i\alpha} Ž A – iB = 1+iα1−iα\frac{1 + i\alpha}{1 - i\alpha}

Ž (A + iB) (A – iB) = (1+iα1−iα)\left( \frac{1 + i\alpha}{1 - i\alpha} \right) = 1

Ž A2 + B2 = 1