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  4. The conjugate of the complex number ((1+i)2/1-i) is

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Q. The conjugate of the complex number $ \frac {(1+i)^2}{1-i}$ is

KCETKCET 2007Complex Numbers and Quadratic Equations

Solution:

Given complex number is $\frac{(1 + i)^2}{1 - i}$
$= \frac{\left(1+ i^{2} +2 i\right)}{1-i} \times \frac{1+i}{1+i} $
$ = \frac{2i\left(1+i\right)}{1-i^{2}} $
$ = \frac{2 i +2i^{2}}{1+1} =\frac{2i-2}{2} $
= i - 1
$\therefore $ Required conjugate is $ -1-i$