Q93 / 180 · COMEDK 2020 · Mathematics

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

  • A
    $1+i$
  • B
    $1-i$
  • Correct answer
    C
    $-1-i$
  • D
    $-1+i$

Solution

Let $Z=\frac{(1+i)^{2}}{1-i}=\frac{1+i^{2}+2 i}{1-i}=\frac{2 i}{1-i} \times \frac{1+i}{1+i}$ $$ =\frac{2 i+2 i^{2}}{1-i^{2}}=\frac{2 i-2}{1+1}=\frac{2 i-2}{2}=-1+i $$

Hence, the correct answer is option: 'C'.

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