Question

{(1+i)/(1-i)}^2 write in form of a+ib​

Answer 1

Answer:

1+

${\frac{1 + i}{1 - i }^{2} } = i {}^{2}$

$\: \: \: \: \: \: \: \: \: = - 1$

$\: \: \: \: \: \: \: \: \: \: = - 1 + 0i$

Answer 2

Given expression,

$\sf{ (\frac{1 + i}{1 - i}) {}^{2} }$

Expanding the terms,

$\sf{ \frac{1 + i {}^{2} + 2i }{1 + i {}^{2} - 2i} } \\ \\ = \sf{\frac{1 - 1 + 2i}{1 - 1 - 2i}} \\ \\ = \sf{ \frac{ - 2i}{2i} } \\ \\ = \huge{\sf{-1 + 0i}}$