3. If $z$ is a complex number with a non-zero real part, then the minimum value of $\frac{\operatorname{Re}\left(z^{4}\right)}{(\operatorname{Re}(z))^{4}}$ is $\qquad$
3. -8

Analysis: Let $z=x+y i(x \neq 0)$, then
$$
\frac{\operatorname{Re}\left(z^{4}\right)}{(\operatorname{Re} z)^{4}}=\frac{x^{4}-6 x^{2} y^{2}+y^{4}}{x^{4}}=\frac{\left(y^{2}-3 x^{2}\right)^{2}-8 x^{4}}{x^{4}} \geq \frac{-8 x^{4}}{x^{4}}=-8
$$

Equality holds if and only if $y= \pm \sqrt{3} x$, hence the minimum value is -8