Science:Math Exam Resources/Courses/MATH152/April 2022/Question A20/Statement

Let ${\textstyle A}$ be a ${\textstyle 2\times 2}$ matrix with eigenvalues ${\textstyle 1+i}$, ${\textstyle 1-i}$. Find ${\textstyle A^{4}}$. (Hint: how does ${\textstyle A^{4}}$ transform the eigenvectors?)