4. Given $z \in C$ and the ratio of the real part to the imaginary part of $(z+5)^{2}$ is $-\frac{3}{4}$, then the range of values for $z$ that satisfy the condition is $\qquad$ .
Answer: $\left\{x+y i \left\lvert\,(x+2 y+5)\left(x-\frac{y}{2}+5\right)=0 \cap((x+5) y \neq 0)\right.\right\}$
Difficulty: Easy
Assessment: Complex Numbers
Analysis: Let $z=x+y i(x, y \in R)$,
then $(z+5)^{2}=(x+5+y i)^{2}=\left(x^{2}+10 x+25-y^{2}\right)+y(2 x+10) i$
By the problem, $\frac{x^{2}+10 x+25-y^{2}}{y(2 x+10)}=-\frac{3}{4} \Leftrightarrow(x+2 y+5)\left(x-\frac{y}{2}+5\right)=0 U((x+5) y \neq 0)$
Therefore, the range of values for $z$ that satisfy the condition is $\left\{x+y i \left\lvert\,(x+2 y+5)\left(x-\frac{y}{2}+5\right)=0 \cap((x+5) y \neq 0)\right.\right\}$