Có bao nhiêu số phức z thỏa mãn z^2/z - 2i = |z^2|

ĐK: $z\ne 2i.$

Ta có:

$\frac{z^2}{z-2i}=\left|z^2\right|\iff \frac{z^2}{z-2i}={\left|z\right|}^2=z.\overline{z}$

$\iff z\left(\frac{z}{z-2i}-\overline{z}\right)=0\iff \left[\begin{array}{l}z=0\left(tm\right)\\ \frac{z}{z-2i}-\overline{z}=0\left(*\right)\end{array}\right.$

Đặt $z=x+yi\Rightarrow \overline{z}=x-yi,$ thay vào (*) ta có

$x+yi=\left(x-yi\right)\left(x+yi-2i\right)$

$\iff x+yi=x^2+xyi-2xi-xyi+y^2-2y$

$\iff x+yi=x^2+y^2-2y-2xi$

$\iff \left\{\begin{array}{l}{x}^2+y^2-2y=x\\ y=-2x\end{array}\right.$

$\iff \left\{\begin{array}{l}{x}^2+4x^2+4x=x\\ y=-2x\end{array}\right.$

$\iff \left\{\begin{array}{l}5x^2+3x=0\\ y=-2x\end{array}\right.$

$\iff \left[\begin{array}{l}x=0;y=0\\ x=-\frac{3}{5};y=\frac{6}{5}\end{array}\right.$

$\Rightarrow \left[\begin{array}{l}z=0\\ z=-\frac{3}{5}+\frac{6}{3}i\end{array}\right.$

Vậy có 2 số phức z thỏa mãn.

Chọn D.