Simplify by multiplying first bracket with the other bracket
(1-i)*(1-i) FOIL
1-i-i+i^2
1-2i+i^2
you said i^2=-1
subsituite
1-2i+(-1)
Combine like terms
-2i+0 = -2i
Simplify \(\dfrac{1 - i}{1 + i}\), where \(i^2 = -1\).
\(\begin{array}{|rcll|} \hline && \mathbf{ \dfrac{1 - i}{1 + i} } \\\\ &=& \left(\dfrac{1 - i}{1 + i} \right)\times \left(\dfrac{1 - i}{1 - i}\right) \\\\ &=& \dfrac{(1 - i)^2}{(1 + i)(1-i)} \\\\ &=& \dfrac{1^2-2i+i^2}{1^2-i^2} \quad & | \quad i^2 = -1 \\\\ &=& \dfrac{1^2-2i-1}{1^2+1} \\\\ &=& \dfrac{ -2i }{2} \\\\ &=& \mathbf{-i} \\ \hline \end{array}\)