Đặt \(z=x+yi\)
\(\left|z-3i\right|=\left|1-i\overline{z}\right|\Rightarrow\sqrt{x^2+\left(y-3\right)^2}=\sqrt{x^2+\left(1-y\right)^2}\)
\(\Rightarrow-6y+9=-2y+1\Rightarrow y=2\) \(\Rightarrow z=x+2i\)
Khi đó: \(z-\dfrac{9}{z}=x+2i-\dfrac{9}{x+2i}=x+2i-\dfrac{9\left(x-2i\right)}{x^2+4}=x-\dfrac{9x}{x^2+4}+\left(2+\dfrac{2}{x^2+4}\right)i\)
Số phức đã cho thuần ảo khi:
\(x-\dfrac{9x}{x^2+4}=0\Rightarrow\left[{}\begin{matrix}x=0\\x=\pm\sqrt{5}\end{matrix}\right.\) \(\Rightarrow z=\left\{2i;\sqrt{5}+2i;-\sqrt{5}+2i\right\}\)
Đúng 0
Bình luận (0)
