Question

Simplify: i^24

Answer 1

i = sqrt of -1. So what is i^2?

Answer 2

-1^2?

Answer 3

It'll just be -1. Square and square root will cancel

Answer 4

Then, if you square it again, you get positive 1. So i^4 equals 1. This repeats every 4. I.e, i^8 is the same as i^4 and so on. What is i^24?

Answer 5

positive 1?

Answer 6

Yes

Answer 7

You can reduce powers of the imaginary unit modulo 4.

Answer 8

$$24\equiv 0 \text{ mod 4}$$ so i^24=i^0=1

Answer 9

what if its an odd number like t^9 @Eads737

Answer 10

Is the question just simplify t^9?

Answer 11

yah

Answer 12

I'm not sure what t is equivalent to. I.e. I know i is sqrt -1, but I'm afraid I don't know what t is so I'm not sure, sorry.

Answer 13

its all good, i just figured it out, thanks though!!!!!!

Answer 14

What is it? and no problem!

Answer 15

The powers of i cycle themselves through the values i, -1 , -i, and 1 so its i then t^2=-1, t^3= -i t^4=1, t^5=i, t^6= -1, and on and on!!!

Answer 16

So t is the same as i in this instance?

Answer 17

yah sorry i don't know why i put t instead of i

Answer 18

Haha, alright