How could you use the answers in part a to find powers of i larger than 4, without multiplying them out

Question

TheSmartOne · Answer

Welcome to QuestionCove!

What was your answer in part a?

TheSmartOne · Answer

Do you know the power rules?

That is what happens to the exponents when you multiply them

kiyaR · Answer

Find i2, i3, and i4. that was my question and my answer i got was -1, -i, 1

TheSmartOne · Answer

Aha, yes of course

So really quickly and simply, can you find

$i^5$
$i^6$
$i^7$
$i^8$

TheSmartOne · Answer

You should notice a very obvious pattern then

kiyaR · Answer

so do you want me to slove what you put up there

TheSmartOne · Answer

Yes please!

You can do it faster if you remember because i^4 = 1

so i^5 = i^4 * I

And similarly for the other ones

payton · Answer

trust them, they are a genious!! XD

kiyaR · Answer

thanks

payton · Answer

yw

TheSmartOne · Answer

@kiyaR were you able to get it?

for example

i^6 = i^4 * i^2

And you already know what i, i^2, i^3, i^4 are from your previous question

kiyaR · Answer

yes and I do thank you for helping me get thur it @the smart one you where such a great help

TheSmartOne · Answer

Of course! And in case you need any more clarification, there's a wonderful article that tells you it probably better than I could have on KhanAcademy https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/a/powers-of-the-imaginary-unit

TheSmartOne · Answer

If you have any other questions, feel free to post them and tag me!

kiyaR · Answer

thanks

TheSmartOne · Answer

My pleasure:)

kiyaR · Answer

I will make sure

kiyaR · Answer

In A Midsummer Night’s Dream, the mention of _____ is an allusion to earlier English poetry.

TheSmartOne · Answer

oh my, it's been years since I've read that play. Are there answer choices given?

kiyaR · Answer

yes  i will give it to you

kiyaR · Answer

Cupid
Demetrius
Lysander
Titania

TheSmartOne · Answer

mhmm just searched it up and read about it, do you have any idea?

kiyaR · Answer

no not really it gave me an answer and on my odysseyware it say's that  it's wrong  b/c i chose cupid

TheSmartOne · Answer

Cupid was wrong? oh boi
that's what everyone else was saying it was

kiyaR · Answer

i think it's right i'll try again

kiyaR · Answer

thanks anyway

TheSmartOne · Answer

Sure thing!