Question

[Hai Nguyên]

Cho số phức z thỏa mãn

|z²-5+12i|=12 tìm max |z|.

Answer 1

[Nguyễn Việt Lâm]

\(12=\left|z^2-\left(5-12i\right)\right|\ge\left|z^2\right|-\left|5-12i\right|=\left|z\right|^2-13\)

\(\Rightarrow\left|z\right|^2\le12+13=25\Rightarrow\left|z\right|\le5\)

\(\Rightarrow\left|z\right|_{max}=5\)