e to the power iota

[ecefag]

hey guys, pls help me out! i want to calculate the value of 'e to the power iota' in c. how can i do it?

[cnoeval]

pow(2.7, 10)???

[ecefag]

why have you taken the power as 10?? :o
the power i have mentioned is iota(square root of -1).

[cnoeval]

iota is the name of the Greek numeral '10'.

For the imaginary number "i" you could use pow(e, -1/-2) I guess but I believe the results would be meaningless without the complex part considered. The math is beyond me, perhaps someone else can help.

[webJose]

Well, in my 6 math courses at the university I never saw eⁱ. The courses went all the way up to differential and integral calculus in multiple variables and equation resolution via numeric methods. So I am completely lost too. I wonder if the calculation is even possible and I wonder more about its application.

[kev82]

Someone's theorem, I forget who (De'Moivre?)

e^{ix} = cos x + i*sin x

So you could calculate the real part with

cos(1.0d)

and the imaginary part with

sin(1.0d)

@webJose

Really, you've never seen e^{ix} at university? In UK, I studied that in A-level. Don't know what equivalent is, but A-level is in school from 16-17 years old.

[m4ster r0shi]

You can use this -> http://en.wikipedia.org/wiki/Euler%27s_formula_in_complex_analysis

Useful links -> [ http://cplusplus.com/reference/clibrary/cmath/ | http://cplusplus.com/reference/std/complex/ ]

EDIT: I need to refresh more frequently...

[webJose]

Really, I never saw it. This is the first time I've seen it mentioned. Do you know of any practical equations that use this? Maybe in electricity? That is one area I barely touched.

[D80DSL3A]

Have you worked much with complex numbers?
In polar notation a complex number z = x + iy = |z|*e^ia
where a = angle off x axis = atan(y/x).

Quiz: What are the 3 principal cube roots of 1?
hint: Two of them are complex.

[ecefag]

i have a formula with me related to ocean acoustics. formula is of channel transfer function. it is:

H(l,f)= summation sign (from p=0 to p-1)Γp/A(lp, f)e−j2πfτp

here j is iota(i) only.

[webJose]

I have used polar coordinates before, but I always worked them in terms of trigonometric functions. I think I was never introduced to the exponential equivalent. Pretty darn interesting.

And no, I have done almost no work with complex numbers. They were limited to the basic (and only) electricity course that I took.

The cube roots are interesting too, but I never studied them (or the nth root).

[m4ster r0shi]

cnoeval wrote:

the name of the Greek numeral '10'

That would be δέκα, pronounced the (just like the before a consonant) - ca (as in cat).

The greek name of i is γιώτα, pronounced jo (as in mjollnir) - ta (as in tank).

EDIT: mjollnir is pronounced myawlneer