How do you simplify #i^42#?

1 Answer
Nov 9, 2015

The imaginary number #i# can only take on 4 values when raised by a positive integer exponent.

Explanation:

#i^1=i#
#i^2=-1#
#i^3= -i#
#i^4=1#

Then, it simply cycles through the same values all over.

To find #i^42# just divide the exponent by 4 and find the remainder :

#42/4 = 10# with a remainder of 2. So, the value 2 is the exponent.

Answer: #i^2=-1#

Hope that helped