Question 170946
This is a cycle: the first two are just definitions of complex numbers so i=i
and {{{i^2=-1)}}}...if you take the sqrt of both these terms you get {{{i=sqrt(-1)}}} that is where they come up with {{{i^2=-1}}}




{{{i=i}}}
:
{{{i^2=-1}}}
:
{{{i^3=i^2(i)=(-1)i=-i}}}
:
{{{i^4=i^2i^2=(-1)(-1)=1}}}
:
then {{{i^5}}} is just {{{i^4(i)=i}}} and it just keeps up this pattern