Question

If a complex number z satisfies the equation $z+\sqrt{2}|z+1|+i=0,$ where $i=\sqrt{-1}$, then $|z|$ is equal to.

• A. $1$
• B. $2$
• C. $\sqrt{3}$
• D. $\sqrt{5}$

Answer 1

The correct option is D $\sqrt{5}$

Put $z=x+iy$, we get $(x+\sqrt{2}\cdot \sqrt{(x+1{)}^2+y^2})+i(y+1)=0+i0$

$\therefore$ On equating real and imaginary parts, we get $x+\sqrt{2}\cdot \sqrt{(x+1{)}^2+y^2}=0$ ..(i)

and $y+1=0$ (ii)

So, on solving (i) and (ii), we get

$x=-2,y=-1$

$\therefore z=-2-i\Rightarrow |z|=\sqrt{5}$.