# Maths - Sqrt of i

Discussion in 'General Discussion' started by MumboJumbo, 24 Apr 2011.

1. MumboJumbo

# Posts: 8,196

Hey, well doing some maths work atm and i've got a sqrt(i) and wondering if I can cancel that down into anything, for instance 1/i = -i etc.

I'm thinking it can't be cancelled down but I thought i'd ask anyway as I may have just missed something simple. Currently my thought process is at the fact that i^5 = i but that's not really particularly helpful with a sqrt.

3. MumboJumbo

# Posts: 8,196

good find, I didn't get anything when I googled. I think I shall leave it at sqrt i.

Am finding the residues of functions so can evaluate their integral using cauchy's residue formula if you know what that is. It's second year uni maths and I'm getting some strange answers and I'm not sure if it's just my lecturer trying to throw me but I've never actually had sqrt's of i in answers for this before. I suppose I will know when I get to the end and have the answer for the integral as the answer has to come out real, though looking at it i'm thinking it won't. hmmm.

4. MumboJumbo

# Posts: 8,196

Yup i've made a mistake. Sod it.

5. jak731

6. MumboJumbo

# Posts: 8,196

7. marc_howarth

# Location: Matlock

sqrt(i) = sqrt(2)/2 + sqrt(2)/2 * i

8. MumboJumbo

# Posts: 8,196

Yeah I've just discovered that from the looks of it. I take it that comes from using de morives? Oh how ever his name is spelt. I should have just done that tbh.

Haha true, you would just presume you'd get a complex answer.

Last edited: 24 Apr 2011
9. MumboJumbo

# Posts: 8,196

thats briliant, using that conversion should make my integral answers real now. Cheers

10. marc_howarth

# Location: Matlock

No problem, doing similar problems myself at the moments. These evaluation of integral questions are HARD!

It's a simple derivation:
let z^2 = i
(a+ib)^2 = i
expand and equate real and imaginary parts.
you should get two equations for a and b
a^2 - b^2 = 0
2ab = 1

simples.

11. MumboJumbo

# Posts: 8,196

Is that so? What uni you at? Leeds by any chance? Second year? Yeah I just got a nice answer of pi/sqrt(2) which sounds very mathy and nice haha.

Nicely done, is very simples.

12. marc_howarth

# Location: Matlock

Up at Edinburgh uni, third (of 4) year. The questions set seem to have a lovely habit of simlifying very nicely, ML Lemma basically making everything go to zero along certain contours.

I'm pretty sure the exam will have a relatively nice first question followed by a big integral evaluation question followed by a PDE with fourier transform question. I'm personally not a fan of PDEs (who is?) and therefore need to make sure I can do integral evaluation well.

13. MumboJumbo

# Posts: 8,196

Dammit, I was so hoping for Leeds though Edinburgh is a nice uni. I've been lumbered with two lecturers who literally don't understand how to teach nor give notes that correspond to the questions they set for fluid dynamics and markov theory. Quite concerned I'm going to fail them .

I'm not sure i've covered ML Lemma yet. Tbh I don't even know any of the first semester analysis work, that lecturer was useless as well. Leeds was meant to be good for teaching but people are dropping out like flies of most of the courses because the lectures are so damn useless in second year! I was going to do the masters as well but I'm not sure I'll bother now.

Haha I don't even really understand what the point of fourier transform's are but I don't mind them too much. Depends how the question is, though yours is probably alot harder than mine.