# A Level Further Maths Powers of i- complex numbers

Watch
Announcements
#1
how do you work out powers of i say for example I^251 without a calculator like this homework I have got is asking
0
1 month ago
#2
(Original post by liamlarner)
how do you work out powers of i say for example I^251 without a calculator like this homework I have got is asking
Break it down, so if I had i^6 for example, using the rule of indices, I would do i^6= (i)^3 x(i)^3, I think for bigger powers it would be much exhausting, but good luck 0
1 month ago
#3
(Original post by liamlarner)
how do you work out powers of i say for example I^251 without a calculator like this homework I have got is asking
Every 4th power of i is 1 since i^4 = 1.

So you might want to rewrite 251 in the form 4k + r where k is an integer and r<4 is the remainder.

Then we have: i^251 = i^(4k+r) = (i^4)^k i^r = i^r

TLDR; i to any power is equivalent to i raised to the remainder when dividing the power by 4.
0
#4
(Original post by RDKGames)
Every 4th power of i is 1 since i^4 = 1.

So you might want to rewrite 251 in the form 4k + r where k is an integer and r<4 is the remainder.

Then we have: i^251 = i^(4k+r) = (i^4)^k i^r = i^r

TLDR; i to any power is equivalent to i raised to the remainder when dividing the power by 4.
this is hella confusing me is their an easier way to do it maybe binomial expansion
0
1 month ago
#5
(Original post by liamlarner)
this is hella confusing me is their an easier way to do it maybe binomial expansion
Seriously?

Example: i^18 … divide 18 by 4 to get remainder 2 … so i^18 = i^2 = -1
1
#6
(Original post by RDKGames)
Seriously?

Example: i^18 … divide 18 by 4 to get remainder 2 … so i^18 = i^2 = -1
ah that example helps so if you have i^253 then, 253 = (4x63)+1 so i^253=i
0
1 month ago
#7
i^2=-1, i^250=-1^125, negative power so stays as -1 as with a positive power it’d be 1. Then multiply -1 by i^1 cos you got 1 left and you getttttttttt -i
0
X

new posts Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

Yes (125)
86.81%
No (19)
13.19%