College Algebra, Chapter 1, 1.4, Section 1.4, Problem 34

Evaluate the expression $i^{1002}$ in the form of $a + bi$.


$\begin{equation} \begin{aligned} &= i^{1002}\\ \\ &= i^{1000+2}\\ \\ &= i^{1000} \cdot i^2\\ \\ &= (i^2)^{500} \cdot i^2\\ \\ &= (-1)^{500} \cdot i^2\\ \\ &= i^2\\ \\ &= -1 \end{aligned} \end{equation}$