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  • If ((1+i)/(1-i))^x=1, then A. x = 2n + 1 B. x = 4n C. x = 2n D. x = 4n + 1

If \left ( \frac{1+i}{1-i} \right )^{x}=1 , then
A. x = 2n + 1
B. x = 4n
C. x = 2n
D.x = 4n + 1

Answers (1)

The answer is the option(b).

\begin{array}{c} \left(\frac{1+i}{1-i}\right)^{x}=1 \\\\ \left(\frac{(1+i)(1+i)}{(1-i)(1+i)}\right)^{x}=1 \\\\ \left(\frac{1-1+2 i}{1+1}\right)^{x}=1 \\\\ \left(\frac{2 i}{2}\right)^{x}=1(i)^{x}=1 \end{array}

x = 4 n, n \epsilon N

Hence, the correct option is b.

Posted by

infoexpert21

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