Mathematics - Complex Number Question with Solution | TestHub

Let $z=a+ib$.

$$\begin{array}{rl}& \Rightarrow a+ib+\sqrt{a^2+b^2}=2+8i\\ & \Rightarrow b=8,a+\sqrt{a^2+64}=2\\ & a^2+64=a^2-4a+4\\ & \Rightarrow -4a=60\\ & \Rightarrow a=-15\\ & \therefore |z|=\sqrt{a^2+b^2}=\sqrt{225+64}=\sqrt{289}=17\end{array}$$