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# how to simplify this imaginary number (exponents)?

4i^6 + i^103

i meaning imaginary not a variable

i get you break it down and like i^2=-1 and stuff

i just dont know HOW you go about breaking it down

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- GreywolfLv 68 years agoFavorite Answer
every i^4 = 1

so i^6 = i^4*i^2 = 1 * -1

i^103 = i^100*i^3 = 1*i^3

-4 + -i

- chesneyLv 44 years ago
For integer exponents, use the homes that i^2 = -1 and i^4 = 1. Signify the integer exponent as a a couple of of four plus a remainder: i^forty six = i^(four*11 + 2) ..And use ordinary homes of exponents: = (i^4)^11 + i^2 = 1^11 + (-1) = -1 in the event you grow to be with a remainder of i^3 on one more problem, don't forget that's (i^2)(i) = (-1)i = -i. For arbitrary powers of i, you can have to wait except you have noticeable De Moivre and Euler theorems to get: i^x = cos(πx/2) + i sin(πx/2) .... πx/2 assumed to be in radians

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