fun with square

3-th square of (-125):

$$\\\sqrt[3]{-125}=\sqrt[3]{125}\times\sqrt[3]{-1}=(5)* \left\{ e^{i\frac{1}{3}(\pi+0*\pi)}, e^{i\frac{1}{3}(\pi+2*\pi)}, e^{i\frac{1}{3}(\pi+4*\pi)} \right\}\\ \sqrt[3]{-125}=(5)* \left\{ e^{i\frac{1}{3}\pi}, e^{i\frac{3}{3}\pi}, e^{i\frac{5}{3}\pi} \right\}\\ \sqrt[3]{-125}=(5)* \left\{ e^{i\frac{1}{3}\pi}, e^{i\pi}, e^{i\frac{5}{3}\pi} \right\}\\ \boxed{e^{i\pi}=-1}\\ \sqrt[3]{-125}=(5)* \left\{ e^{i\frac{1}{3}\pi}, -1, e^{i\frac{5}{3}\pi} \right\}\\ \\ \sqrt[3]{-125}=(5)* e^{i\frac{1}{3}\pi} \quad \text{complex number} \\\\ \sqrt[3]{-125}=(5)*(-1)=-5\quad \text{real number }\\\\ \sqrt[3]{-125}=(5)* e^{i\frac{5}{3}\pi} \quad \text{complex number} \\$$