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

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Medium

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Application +4 | -1

\frac{1-i \alpha}{1+i \alpha}=A+i B

, then

A^2+B^2

equals

View answer and explanation

Correct option: A

Option A (1) is correct because the magnitude of a complex number divided by its conjugate is always 1.

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{\left| {1 - i} \right|^x} = {2^x}

|z|=1

z \neq \pm 1

z, \frac{z}{1-z^2}

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

\left|\sum\limits_{r=1}^n z_r\right|

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a \neq 0

\alpha, \beta

\gamma

|\alpha-\beta|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

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