Question

The complex number $z$ satisfies $z+|z|=2+8i$. The value of $|z|$ is

• A. $10$
• B. $13$
• C. $17$
• D. $23$

Answer 1

The correct option is C $17$

$Assume,z=a+ib,wherei=\sqrt{-1}$

$Then,z+|z|=a+ib+\sqrt{a^2+b^2}=2+8i$

$Thus,b=8.$

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

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

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

$a=-15$

$Thusz=-15+8i$

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