Q71 / 150 · MHT CET 2021 (20 Sep Shift 1) · Mathematics

The value of $(1+i)^5(1-i)^7$

  • A
    -64
  • Correct answer
    B
    -64 i
  • C
    64 i
  • D
    64

Solution

$\begin{aligned} & (1+i)^5(1-i)^7 \\ = & (1+i)^5(1-i)^5(1-i)^2=[(1+i)(1+i)(1-i)]^5\left(1-2 i+i^2\right) \\ = & \left(1-i^2\right)^5(-2 i)=(2)^5(-2 i)=-64 i \ldots\left[\because i^2=-1\right]\end{aligned}$

Hence, the correct answer is option: 'B'.

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