How do you simplify #i^10+i^2#?

1 Answer
Dec 3, 2016

The expression simplifies to #-2#.

Explanation:

#i^10 + i^2#

Use the exponent rule #(x^a)^b= x^(ab)# and change the #i^10# term to an #i^2# term by dividing the exponent #color(blue)(10)# by #color(red)2=color(magenta)5#.

#i^color(blue)(10)=(i^color(red)2)^color(magenta)5#

#(i^2)^5+i^2#

Recall that #i^2=-1#

#(-1)^5 +(-1)#

#-1# raised to an odd power is equal to #-1# (and btw, #-1# raised to an even power is equal to #1#)

#(-1) +(-1)=-2#