Question 1177965
<br>
{{{(1-i)^2 = 1-2i+i^2 = -2i}}}
{{{1/(1-i)^2 = 1/-2i = (1/2)i}}}<br>
The problem also gives you an opportunity to practice the use of deMoivre's Theorem, which is a very powerful tool.<br>
Convert each complex number to A*cisB form.<br>
{{{1 = 1cis(0)}}}
{{{1-i = sqrt(2)cis(-45)}}}<br>
Square the second one using deMoivre's Theorem.<br>
{{{(1-i)^2 = (sqrt(2)cis(-45))^2 = 2cis(-90)}}}<br>
Perform the division using deMoivre's Theorem.<br>
{{{1/(1-i)^2 = 1cis(0)/(2cis(-90)) = (1/2)cis(90) = (1/2)i}}}<br>