Question

giai pt:|z| + z=3+4i

Answer 1

goi \(z=a+bi\)

\(\Rightarrow\)\(\left|z\right|+z=3+4i\Leftrightarrow\sqrt{a^2+b^2}+a+bi=3+4i\)

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{a^2+b^2}+a=3\\b=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}3-a\ge0\\a^2+b^2=\left(3-a\right)^2\end{matrix}\right.\\b=4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=\dfrac{-7}{6}\\b=4\end{matrix}\right.\Rightarrow z=\dfrac{-7}{6}+4i\)