Question

Simplify i^31

Answer 1

What is the remainder if you divide 31 by 4?

Answer 2

as in i = sqrt -1...?
if so, then for every even power : =1
for every 2nd odd power = -i or i (alternating)

Answer 3

so -i?

Answer 4

yep

Answer 5

not equal to 1 for all even powers, @Jack1
i^n is equal to 1 if and only if n is divisible by 4.

Answer 6

example:
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
i^5 = i
...etc

Answer 7

its a repeating system of 4 possible answers,
...sorry, meant to write 1 or -1

Answer 8

so its -1?

Answer 9

Sometimes, I get the feeling you do these on purpose, to provoke, @ParthKohli
:|


haha...
you realise, in the end, it became \(\Large -1\cdot -1 \cdot i= i\)
fail... XD

Answer 10

lol ;D

Answer 11

im so confused what is the answer.

Answer 12

No, it's not that...
Why did you replace \(\large i^{28}\) with \(\large -1\) ?

Answer 13

@MathHelper22 answer = -i

Answer 14

Yes... so
\[\huge i^{28} = 1\]
:/

bloody hell @ParthKohli :D

Answer 15

OOOOOOOOOOOOOOOOOOOOOH MY GAAAAAAAAAAARDH

Answer 16

^picture fits.

Answer 17

@ParthKohli I'm not sure how it could be any clearer dude:
i^28 = 1
i^29 = i
i^30 = -1
i^31 = -i
i^32= 1
...etc

Answer 18

oh I remember this... imaginary numbers

Answer 19

remember when negative square roots aren't allowed? For example

Answer 20

Pepperidge Farm remembers.

Answer 21

LOL! ...Remember when you hit that pedestrian with your car at the crosswalk and then just drove away? Pepperidge Farm remembers...Maybe you go out and buy yourself some of these distinctive Milano cookies, maybe this whole thing disappears...