please solve question 15

Dear Student,

{(\frac{1 + i}{1 - i})}^{x} = 1 \Rightarrow {[\frac{1 + i}{1 - i} \times \frac{1 + i}{1 + i}]}^{x} = 1 \Rightarrow {[\frac{1 + i^{2} + 2 i}{1^{2} - i^{2}}]}^{x} = 1 a s i^{2} = - 1 \Rightarrow {[\frac{1 - 1 + 2 i}{1 + 1}]}^{x} = 1 \Rightarrow {[\frac{2 i}{2}]}^{x} = 1 \Rightarrow i^{x} = 1 a s w e k n o w i^{2} = - 1 a n d i^{4} = 1, h e n c e x = 4 n w h e r e n i s p o s i t i v e i n t e g e r

Regards,