complex numbers - $(sqrt{3} + i)^{50}$ in exponential and cartesian form

Having trouble understanding the solution to the following question:

Put $(\sqrt{3} + i)^{50}$ in exponential and cartesian form.

I know the answer cartesian form is:

$$\frac{2^{50}}{2} + \frac{2^{50}\sqrt{3}}{2}i$$

And the exponential form is:

$$2^{50}e^{\frac{50\pi}{6}i}$$

But I don't know how to get there.

I know that $i^{50} = i^{4(12)+2} = i^2 = -1$. Is that somehow used in the process?
What form is it given in?

Answer

Use the fact that $$\sqrt3+i=2\left(\frac{\sqrt3}2+\frac i2\right)=2\left(\cos\left(\frac\pi6\right)+i\sin\left(\frac\pi6\right)\right),$$ together with de Moivre's formula.