A) \[n=8\]
B) \[n=12\]
C) \[n=16\]
D) none of these
Correct Answer: D
Solution :
Now, \[\frac{1+i}{1-i}=\frac{(1+i)(1+i)}{(1-i)(1+i)}=\frac{1+{{i}^{2}}+2i}{2}=i\] Now, \[{{\left( \frac{1+i}{1-i} \right)}^{n}}=1\] \[\Rightarrow \] \[{{(i)}^{n}}=1\] ???(i) \[\Rightarrow \]Least value of n for which Eq. (i) is true is 4 \[\because \] \[{{(i)}^{4}}=1\]You need to login to perform this action.
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