Polar Coordinates and Complex Numbers · Challenge problem

The equation $z^4 + 4 = 0$ has four complex solutions. Find the sum of the squares of their distances from the point $1$ (that is, find $\left|z_1 - 1\right|^2 + \left|z_2 - 1\right|^2 + \left|z_3 - 1\right|^2 + \left|z_4 - 1\right|^2$).