Hans Georg Schaathun
September 2016
$$x^2 = y$$
$$x = \pm\sqrt y$$
$$y < 0 \quad\Longrightarrow\quad\text{inga løysing}$$
$$w^2 = z = r(\cos\theta+i\sin\theta)$$
$$w = \sqrt r\bigg(\cos\frac\theta2+i\sin\frac\theta2\bigg)$$
$$w^2 = r(\cos\theta+i\sin\theta)$$
$$w = \sqrt r\bigg(\cos\big(\pi+\frac\theta2\big)+i\sin\big(\pi+\frac\theta2\big)\bigg)$$
$$z=w^n = r(\cos\theta + i\sin\theta)$$
$$w = \sqrt[n]{r}\bigg(\cos\frac{\theta}{n} + i\sin\frac{\theta}{n}\bigg)$$