Chapter 1 - Equations and Inequalities - 1.3 Complex Numbers - 1.3 Exercises - Page 113: 100

$1$

Apply exponent rule: $\displaystyle \quad a^{-n}=\frac{1}{a^{n}}$ $\displaystyle \frac{1}{i^{-12}}=\frac{1}{(\frac{1}{i^{12}})}=i^{12}$ $ i^{12}\qquad$...Apply exponent rule: $\quad a^{bc}=(a^{b})^{c}$ $=(i^{2})^{6}\qquad$...Apply imaginary number rule: $\quad i^{2}=-1$ $=(-1)^{6}\qquad$...Apply exponent rule: $(-a)^{n}=a^{n},$ if $n$ is even. $=1^{6}$ $=1$