Complex Numbers - Applying Complex Conjugate Identities

\({z={{\left( a+b\mathbf{i} \right)}^{4n}}+{{\left( b+a\mathbf{i} \right)}^{4n}}}\), \({a\in \mathbb{R}}\), \({b\in \mathbb{R}}\), \({n\in \mathbb{N}}\).

Show that \({z}\) is a real number.