Question 170946
"Imaginary" Numbers (i), an unfortunate nomenclature, are based on {{{sqrt(-1)}}}.
{{{i = sqrt(-1)}}}={{{i}}} 
{{{i^2 = (sqrt(-1))^2}}}={{{-1}}}
{{{i^3 = (sqrt(-1))^3}}}={{{(sqrt(-1))^2*(sqrt(-1)) = -1*i}}}={{{-i}}} 
{{{i^4 = (sqrt(-1))^4}}}={{{(sqrt(-1))^2*(sqrt(-1))^2 = (-1)(-1)}}}={{{1}}}
{{{i^5 = (sqrt(-1))^5}}}={{{(sqrt(-1))^2*(sqrt(-1))^3 = -1*(-i)}}}= {{{i}}}
Can you begin to see a pattern here?