What is the simplified version of #i^20sqrt(-196)#?

1 Answer
LM
Jan 26, 2018

#14i#

Explanation:

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

the powers of #i# have a cyclic pattern, repeating every #4#th power.

#i^20 = i^(4 * 5) = i^4 = 1#

#i^20sqrt(-196) = 1 * sqrt(-196)#

#= sqrt(-196)#

#sqrt(-196) = 14i#

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