# Sequence limit with complex numbers, where $u_n=\Re(({\frac{1+i\sqrt{7}}{2}})^n)$ [duplicate]

How do you prove :

$$\forall n \in \mathbb{N}$$ if $$u_n=\Re(({\frac{1+i\sqrt{7}}{2}})^n)$$ where $$\Re$$ mean the real part of a complex number, that $$\lim_{n\rightarrow +\infty}\left | u_n \right |=+\infty$$

$$\left | u_n \right |$$ is the modulus of $$u_n$$