If $z = x + iy$, then the value of $\displaystyle \lim_{x \to 3 - 4i} \dfrac{i~\text{Re}(z)^2}{|z|}$ is....
My attempt: I get that the function of the limit should be $\dfrac{i~(x^2 - y^2)^2}{\sqrt{x^2 + y^2}} $ after we substitute $|z| = \sqrt{x^2 + y^2}$ and $\text{Re}(z)^2 = (x^2 - y^2)^2$, but I can't continue after this step. If we substitute $x$ so what the limit wants, then it leads to more complicated form. Please, could you help me?