Question

The complex number $z$ satisfies $z+|z|=2+8i$, then the value of $|z|$ is

• A. $17$
• B. $16$
• C. $13$
• D. $9$

Answer 1

The correct option is A $17$

Assume $z=a+ib$ $;i=\sqrt{-1}$

so $z+\left|z\right|=2+8i$

$a+ib+\sqrt{a^2+b^2}=2+8i$

Here $b=8$

$a+\sqrt{a^2+64}=2$

$a^2+64=(2-a{)}^2$

$a^2+64=4+a^2-4a$

$a=-15$

$z=-15+8i$

so $\left|z\right|=\sqrt{(-15{)}^2+8^2}=17$