# Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set: 99

$0$

#### Work Step by Step

RECALL: (1) $a^{mn} = (a^m)^n$ (2) $i^2=-1$ (3) $a^{m+n} = a^m \cdot a^n$ Use rule (1) above to obtain: $=(i^2)^{12}+i^2$ Use rule (2) above to obtain: $\\=(-1)^{12}+(-1)$ Note that when $-1$ is raised to an even power, the result is $1$. Thus, the expression above simplifies to: $=1 + (-1) \\=0$

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