How do you simplify #i^803#?

1 Answer
Mar 9, 2018

#i^803=color(red)(-i)#

Explanation:

#i^1=i#
#i^2=-1# (definition)
#i^3=(-1)xxi=-i#
#i^4=(-1)xx(-1)=1#

#i^803=i^800 * i^3#
#color(white)("XX")=(i^4)^200 * i^3#
#color(white)("XX")=1^200 * (-i)#
#color(white)("XX") =1xx(-i)#
#color(white)("XX")=-i#