So im pretty sure i got part 1. 3 is the magnitude and its to the power of (5/6)(pi)i

Please help with the following questions cheers.

Printable View

- May 9th 2013, 07:58 AMBrennoxAnalytic funtions
So im pretty sure i got part 1. 3 is the magnitude and its to the power of (5/6)(pi)i

Please help with the following questions cheers. - May 9th 2013, 08:38 AMebainesRe: Analytic funtions
Hint for 2 and 3:

So:

Hint for 4 and 5:

If , then - May 9th 2013, 10:17 AMBrennoxRe: Analytic funtions
- May 9th 2013, 10:27 AMebainesRe: Analytic funtions
Q2 and Q3 - good!

Yes: - May 9th 2013, 11:05 AMBrennoxRe: Analytic funtions
Thanks heaps, can you please help me with this Q.

i can get part 1 but am really struggling with part 2. Do all values have to be <pi?

heres link. http://oi41.tinypic.com/30mbqqe.jpg - May 9th 2013, 11:36 AMebainesRe: Analytic funtions
No - they range between 0 and 2 pi.

From de Moivre's formula, , the angle of one solution will be 1/n the angle of z. Note that I like to use the notation "cis theta" (pronounced "kiss theta") as shorthand for . But since cosine and sine functons have a period of , other solutions are available that are "evenly spaced" about the origin separated by the angle . In this way there are always n solutions to the nth root of z.

Let me give an example: If z = 16i, which is equal to , there are four 4th roots. The magnitude of z is 16, so the magnitude of the 4th roots are all . The angle of the first solution is at angle , and the rest are at , where k = 0, 1, 2, and 3. Thus the four 4th roots of 16i are: .

Now, can you apply this thinking to the problem at hand? - May 9th 2013, 12:19 PMBrennoxRe: Analytic funtions
- May 9th 2013, 12:34 PMBrennoxRe: Analytic funtions
http://oi43.tinypic.com/34hz2ae.jpg

for part 1 is...

v = e^(5x)cos(5y)

and how do i right an expression for f'(z) when there are x and y - May 9th 2013, 01:08 PMebainesRe: Analytic funtions
Close - check your signs. I get , so:

As for the derivative of a complex function z = u(x,y) + i v(x,y), it's:

- May 9th 2013, 01:14 PMPlatoRe: Analytic funtions
- May 10th 2013, 12:11 AMBrennoxRe: Analytic funtions
thanks heaps, i dont understand why i got this Q wrong tho.

http://oi43.tinypic.com/d4suq.jpg

du/dx = 2x

dv/dy = 2x

du/dy = -2y + 5

dv/dx = -2y + 5

Did i do the wrong input for part 2? "x^2-y^2+5y+9+i(-2xy+5x)" - May 10th 2013, 05:27 AMPlatoRe: Analytic funtions