Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If $(1-i)^n=2^n$, then $n=$
A
1
✓
$0$
C
$-1$
D
4
✓
Answer
Correct option: B.
$0$
(B) $(1- i )^{ n }=2^{ n }$ ...(i) We know that if two complex numbers are equal, their moduli must also be equal,therefore from (i), we have $\left|(1- i )^{ n }\right|=\left|2^{ n }\right|$ $\Rightarrow|1- i |^{ n }=|2|^{ n } \quad \ldots . .\left[\because 2^{ n }>0\right]$ $\Rightarrow\left[\sqrt{1^2+(-1)^2}\right]^n=2^n$ $\Rightarrow(\sqrt{2})^{ n }=2^{ n }$ $\Rightarrow 2^{\frac{n}{2}}=2^n$ $\Rightarrow \frac{ n }{2}= n$ $\Rightarrow n =0$
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