Question

If $(1+i)z=(1-i)\overline{z}$ then $z$ is:

• A. $t(1-i),t\in R$
• B. $t(1+i),t\in R$
• C. $\frac{t}{1+i},t\in R^{+}$
• D. None of these

Answer 1

The correct option is A $t(1-i),t\in R$

Let $z=x+1y,x,y\in R$

Put in equation

$(x+iy)(1+i)=(1-i)(x-iy)$

$x+iy+ix-y=x-iy-ix-y$

$(x-y)+1(x+y)=(x-y)+1(-x-y)$

$\therefore -x-y=x+y$

$\Rightarrow x=-y$

Hence, $z=t(1-i),t\in R$ is correct