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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If n is an odd integer, then $(1+ i )^{6 n }+(1- i )^{6 n }$ is equal to
  • ✓
    $0$
  • B
    2
  • C
    -2
  • D
    1
✓

Answer

Correct option: A.
$0$
(A)
$(1+i)^{6 n}+(1-i)^{6 n}=\left\{(1+i)^2\right\}^{3 n}+\left\{(1-i)^2\right\}^{3 n}$
$=(2 i )^{3 n }+(-2 i )^{3 n }$
$=2^{3 n}\left\{i^{3 n}+(-i)^{3 n}\right\}$
$=0 \quad \ldots .[\because n$ is odd $]$

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