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Model Paper 9 — MATHS STD 11 Science — Question

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

Answer

(a) x = 4n
Explanation: $\Rightarrow\left[\frac{(1+i)(1+i)}{(1-i)(1+i)}\right]^x=1 \Rightarrow\left[\frac{1+2 i+i^2}{1-i^2}\right]^x=1 \Rightarrow\left[\frac{2 i}{1+1}\right]^x=1$
$\begin{array}{l}\Rightarrow I ^{ x }=1 \\ \Rightarrow x =4 n , n \in N \end{array}$

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