Cho số phức z thỏa mãn

B

- Hướng dẫn giải

Đáp án B

$$\begin{gathered} z=x+yi,(x,y\in R) \\ \Rightarrow P={\left(x+2\right)}^2+y^2-x^2-{\left(y-1\right)}^2=4x+2y+3 \\ \left|z-3-4i\right|=\sqrt{5}\iff {\left(x-3\right)}^2+{\left(y-4\right)}^2=5 \end{gathered}$$

Đặt $x=3+\sqrt{5}\sin t, y=4+\sqrt{5}\cos t$ thỏa mãn ${\left(x-3\right)}^2+{\left(y-4\right)}^2=5$

$$\begin{gathered} \Rightarrow P=4\sqrt{5}\sin t+2\sqrt{5}\cos t+23 \\ f\left(t\right)=4\sqrt{5}\sin t+2\sqrt{5}\cos t \\ \frac{f\left(t\right)}{10}=\frac{2\sqrt{5}}{5}\sin t+\frac{\sqrt{5}}{5}\cos t \end{gathered}$$

$$\begin{gathered} Đặt \left\{\begin{array}{l}cosu=\frac{2\sqrt{5}}{5}\\ \sin u=\frac{\sqrt{5}}{5}\end{array}\Rightarrow \frac{f\left(t\right)}{10}=\sin \left(t+u\right)\right. \\ \Rightarrow -1\le \frac{f\left(t\right)}{10}\le 1\Rightarrow -10\le f\left(t\right)\le 10\Rightarrow 13\le P\le 33 \\ \Rightarrow \left|w\right|=\sqrt{1258} \end{gathered}$$