How do you simplify $i^42$ ?

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Answer 1 · 2015-11-09T00:08:20

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

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

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

How do you simplify i^42i^42?