Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
The smallest positive integer $n$ for which $(1+i)^{2 n}=(1-i)^{2 n}$ is
A
1
✓
2
C
3
D
4
✓
Answer
Correct option: B.
2
(B) We have, $(1+i)^{2 n}=(1-i)^{2 n}$ $\Rightarrow\left(\frac{1+ i }{1- i }\right)^{2 n }=1 \Rightarrow( i )^{2 n }=1$ $\Rightarrow( i )^{2 n }=(-1)^2 \Rightarrow( i )^{2 n }=\left( i ^2\right)^2$ $\Rightarrow( i )^{2 n }=( i )^4 \Rightarrow 2 n =4$ $\Rightarrow n =2$
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