Find the value of complex expression $left(frac{sqrt{3}+i}{2}right)^{69}$

Find the value of

$$\left(\dfrac{\sqrt{3}+i}{2}\right)^{69}.\DeclareMathOperator{\cis}{cis}$$

I tried to solve this complex expression by converting it into polar form.
I expressed it in polar form $r\cis(t)$ from rectangular form $x+iy$ where $\cis(t) = \cos(t) + i\sin(t)$.
But I am unable to solve further due to the exponent of 69!

Answer

$$\left(\dfrac{\sqrt{3}+i}{2}\right)^{69}=\left(\dfrac{\sqrt{3}}{2}+\dfrac{1}{2}i\right)^{69}=(\cos\dfrac{\pi}{6}+i\sin\dfrac{\pi}{6})^{69}=\cos\dfrac{69\pi}{6}+i\sin\dfrac{69\pi}{6}=-i$$
by De Moivre's formula.