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Model Paper 1 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 11 Mark
MCQ
If $z=\left(\frac{1+i}{1-i}\right)$, then $z^4$ equals.
  • A
    $0$
  • B
    -1
  • C
    2
  • D
    1
✓

Answer

(d) 1
Explanation:  1
$\begin{array}{l}\text { Let } z =\frac{1+i}{1-i} \\ 
z=\frac{1+i}{1-i} \times \frac{1+i}{1+i} \\ 
\Rightarrow z=\frac{1+ i ^2+2 i}{1-i^2} \\ 
\Rightarrow z=\frac{2 i}{2}\end{array}$
$\begin{array}{l}\Rightarrow z=i \\ 
\Rightarrow z^4=i^4\end{array}$
Since i2 = -1, we have: 
$\begin{array}{l}\Rightarrow z^4=i^2 \times i^2 \\ 
\Rightarrow z^4=1\end{array}$

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