Q151 / 270 · NDA 2011 (Phase 2) · Mathematics

What is the value of $(1+i)^5+(1-i)^5$ where $i=\sqrt{-1}$ ?

  • Correct answer
    A
    $-8$
  • B
    $8$
  • C
    $8 i$
  • D
    $-8 i$

Solution

$\begin{aligned} & (1+i)^5+(1-i)^5 \\ = & 1+5 c_1 1^4 \cdot i+5 c_2(1)^3(i)^2+5 c_3(1)^2(i)^3+5 c_4(1)(i)^4 \\ & +i^5+1-5 c_1(1)^4 i+5 c_2(1)^3 \cdot(i)^2-5 c_3(1)^2 i^3+5 c_4(1) \\ & (i)^4-i^5 \\ = & 2-10+5-10+5=-8 .\end{aligned}$

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

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