Complex numbers

[kpx001]

hey guys i need help understanding complex numbers. i know that i = sqroot-1 and i^2 = -1 but beyond that i get confused. can someone please explain how to get the answers.

i^3 = 3/2 = 1.5 = -i ?
i^4 = 1
i^5 = 5/2 = 2.5 = i ?

i need help going beyond etc

 

[pka]

I understand what you are doing.
But let me assure you that it is dangerous to you understanding!

Here are the facts: i, i<SUP>2</SUP>=-1, i<SUP>3</SUP>=-i, and i<SUP>4</SUP>=1. It repeats every 4 times.

Thus you need to look at the remainder when divided by 4.
i<SUP>27</SUP>= i<SUP>3</SUP>=-i because 3 is the remainder when 27 is divided by 4.
i<SUP>32</SUP>= i<SUP>0</SUP>=1 because 0 is the remainder when 32 is divided by 4.

 

[kpx001]

thanks that helps a lot, but can u show me a couple problems to get just plain old i?
im guessing i^17 = i^1 = i?

 

[pka]

thanks that helps a lot, but can u show me a couple problems to get just plain old i? im guessing i^17 = i^1 = i?

YES! Way to go!

 

[Mrspi]

thanks that helps a lot, but can u show me a couple problems to get just plain old i?
im guessing i^17 = i^1 = i?

As you were told in previous posts,
i<SUP>1</SUP> = i
i<SUP>2</SUP> = -1
i<SUP>3</SUP> = i<SUP>2</SUP>*i = -1*i = -i
i<SUP>4</SUP> = (i<SUP>2</SUP>)<SUP>2</SUP>) = (-1)<SUP>2</SUP> = 1

So, for i<SUP>17</SUP>, let's find the largest number of factors of i<SUP>4</SUP> that we can (because i<SUP>4</SUP> is just 1):

i<SUP>17</SUP> = (i<SUP>4</SUP>)<SUP>4</SUP>*i
I<SUP>17</SUP> = (1)<SUP>4</SUP>*i, or 1*i, or just i.

You are correct!