Why does i raised to an exponent change when using even numbers? You'd expect that a negative number with an even exponent to always come out positive. Can someone explain the pattern:
i^2= -1, i^4+ 1, i^6= 1, i^8= -1, i^10= 1, and so on. Why does it bounce from negative to positve?
+118608 By definition
$$i=\sqrt{-1}$$
Remember this is not a real number it is an imaginary number!
squares and square roots cancle each other out so
$$\\i^2=(\sqrt{-1})^2 = -1\\\\
i^4=i^2\times i^2=-1\times-1=+1\\\\
i^6=i^4\times i^2=1\times-1=-1\\\\
i^8=i^6\times i^2=-1\times-1=+1\\\\
i^{10}=i^8\times i^2=+1\times-1=-1\\\\$$
does that help you to understand? 
+118608 By definition
$$i=\sqrt{-1}$$
Remember this is not a real number it is an imaginary number!
squares and square roots cancle each other out so
$$\\i^2=(\sqrt{-1})^2 = -1\\\\
i^4=i^2\times i^2=-1\times-1=+1\\\\
i^6=i^4\times i^2=1\times-1=-1\\\\
i^8=i^6\times i^2=-1\times-1=+1\\\\
i^{10}=i^8\times i^2=+1\times-1=-1\\\\$$
does that help you to understand?
