Question

The solution of the equation $\left|z\right|-z=1+2i$ is

• A. $\frac{3}{2}-2i$
• B. $\frac{3}{2}+2i$
• C. $2-\frac{3}{2}i$
• D. None of these

Answer 1

The correct option is A $\frac{3}{2}-2i$

We have $\left|z\right|-z=1+2i$

$\Rightarrow \sqrt{x^2+y^2}-(x+iy)=1+2i$ where $z=x+iy$

$\Rightarrow \sqrt{x^2+y^2}-x=1$ and $y=-2$

$[$Comparing real and imaginary parts$]$

$\Rightarrow x=\frac{3}{2}$ and $y=-2$

$\therefore$ The solution of the given equation is $\frac{3}{2}-2i$.