Find square root of complex number

So for some stupid formula like this:

$$Z_o = \sqrt{\frac{R+j\omega L}{G+j\omega C}}$$

or this

$$\gamma = \sqrt{(R+j\omega L)(G+j\omega C)}$$

How do you calculate the square root of complex number? Here's how:

1. Reduce stuff down to $\sqrt{a + ib}$
2. Convert to angle form using calculator: $intermediate = \sqrt{r\angle\theta}$
3. $intermediate$ can be written as $\sqrt{r} (cos(\frac{\theta}{2}) + i sin(\frac{\theta}{2}))$
4. Reduce that ugly equation back into $a' + ib'$.
5. ???
6. Profit?