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

Question

The conjugate of the complex number ((1+i)2/1-i) is (A) 1 - i (B) 1 + i (C) -1+ i (D) -1 - i

Tardigrade Admin · Accepted Answer

Given complex number is ((1 + i)2/1 - i) = ((1+ i2 +2 i)/1-i) × (1+i/1+i) = (2i(1+i)/1-i2) = (2 i +2i2/1+1) =(2i-2/2) = i - 1 ∴ Required conjugate is -1-i

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

$1 - i$

$1 + i$

$- 1 + i$

$- 1 - i$

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

Q. The conjugate of the complex number 1−i(1+i)2​ is

1−i

1+i

−1+i

−1−i