-i²=

Simplify the following: -i^2 i^2 = -1: --1 (-1)^2 = 1: Answer: | | 1

-i²= ?

$\boxed{~ \begin{array}{lcll} z &=& a+b\cdot i \\ \bar{z} &=& a-b\cdot i\\ z\cdot \bar{z} &=& a^2+b^2 \\ && \text{where } \bar{z} \text{ is the complex conjugate of } z \end{array} ~}$

$\begin{array}{rcll} -i^2 &=& 0-i^2 \\ &=& (0+i)(0-i) \\ &=& \underbrace{(0+i)}_{=z}\cdot \underbrace{(0-i)}_{=\bar{z}} \qquad a = 0 \qquad b = 1 \\ -i^2 &=& 0^2+1^2 \\ -i^2 &=& 1 \\ \end{array}$

i is DEFINED as sqrt(-1)   so  i^2 = -1      -(-1) = 1