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Question: If \(\left( \frac{1 + i}{1 - i} \right)^{x} = 1\) then...

If (1+i1−i)x=1\left( \frac{1 + i}{1 - i} \right)^{x} = 1 then

A

x = 4n, where n is any positive integer

B

x = 2n, where n is any positive integer

C

x = 4n +1, where n is any positive integer

D

x = 2n +1, where n is any positive integer

Answer

x = 4n, where n is any positive integer

Explanation

Solution

Sol. 1+i1−i=1+i1−i.1+i1+i\frac{1 + i}{1 - i} = \frac{1 + i}{1 - i}.\frac{1 + i}{1 + i} ⇒ (1+i1−i)x=1\left( \frac{1 + i}{1 - i} \right)^{x} = 1 ⇒ ix=1i^{x} = 1

⇒ x=4n,n∈I+.x = 4n,n \in I^{+}.