Evaluate $(\sqrt{3}+i)^{14}+(\sqrt{3}-i)^{14}$ Evaluate $(\sqrt{3}+i)^{14}+(\sqrt{3}-i)^{14}$
I tried by using the De'moivers theorem but I didn't get proper value I get a mess value 4..but I am not sure about the answer can anyone please tell me

Observe that
$$
(\sqrt{3} + i)^{14} = ((\sqrt{3} + i)^2)^7
$$
Also, $ (\sqrt{3} + i)^2 = 2 + i 2\sqrt{3} = 2 (2 e^{j\theta}) = 4 e^{j\theta}$, where $ \theta = \pi / 3 $.
Similarly, for the second term we have that $ (\sqrt{3} - i)^2 = 4 e^{-j\theta} $.
You problem reduces to finding 
$$ 
M = 4^7 \cdot e^{j 7\theta} + 4^7 \cdot e^{-j 7\theta}  
= 4^7 \cdot 2 \cdot (\frac{e^{j 7\theta} + e^{-j 7\theta}}{2})  
= 4^7 \cdot \cos(7\theta)
= 4^7 \cdot 1
= 16384
$$ 
