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BITSAT 2010
Exam
BITSAT
Year
2010
Subject
Mathematics
Chapter
Permutation and Combination

BITSAT 2010 · Mathematics · Permutation and Combination

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

If (1−iα1+iα=\frac{1-i \alpha}{1+i \alpha}=A+i B), then A2+B2A²+B² equals to

Options

  1. A1
  2. B(\alpha^2)
  3. C-1
  4. D(-\alpha^2)

Correct answer

A. 1

Step-by-step solution

A+iB=1−iα1+iα\RightarrowA−iB=1+iα1−iα⇒(A+iB)(A−iB)=(1−iα)(1+iα)(1+iα)(1−iα)=1⇒A2+B2=1\begin{aligned}& A+i B=\frac{1-i \alpha}{1+i \alpha} \RightarrowA-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 A²+B²=1 \end{aligned})
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