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Model Paper 9 — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsModel Paper 91 Mark
MCQ
If $\left(\frac{1+i}{1-i}\right)^x=1$, then
  • ✓
    $x = 4n$
  • B
    $x = 2n$
  • C
    $x = 2n+1$
  • D
    $x =4 n +1$, where $n \in N$
✓

Answer

Correct option: A.
$x = 4n$
$\Rightarrow\left[\frac{(1+i)(1+i)}{(1-i)(1+i)}\right]^x=1 $
$\Rightarrow\left[\frac{1+2 i+i^2}{1-i^2}\right]^x=1 $
$\Rightarrow\left[\frac{2 i}{1+1}\right]^x=1$
$\Rightarrow I ^{ x }=1$
$\Rightarrow x =4 n , n \in N $

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