The question says,

Find all splutions of the following equations, expressing your answers in Cartesian form (i.e as z=x+iy)

(a)

Do i simple open it out and simplify?.. is there anything else that needs to be done?

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- Jan 19th 2008, 07:37 AMbrd_7Complex Numbers :D
The question says,

Find all splutions of the following equations, expressing your answers in Cartesian form (i.e as z=x+iy)

(a)

Do i simple open it out and simplify?.. is there anything else that needs to be done? - Jan 19th 2008, 07:51 AMPlato
Find the four fourth roots of .

- Jan 19th 2008, 08:15 AMbrd_7
Oh ok, And how do i go about starting that?

- Jan 19th 2008, 09:09 AMtopsquark
- Jan 19th 2008, 01:24 PMbrd_7

Represent in the form

I got

Let

Then

So

And then-

z^4 = 2.{cos[(1/3 + 2n)pi] + isin[(1/3 + 2n)pi]}. And so

z = 2^[1/4]{cos[(1/12 + n/2)pi] + isin[(1/12 + n/2)pi]].

Is this all right?.. What do i do now?.. How do i change it back to x +iy? - Jan 19th 2008, 01:40 PMPlato
Yes it is correct if this is what you mean.

- Jan 19th 2008, 03:04 PMbrd_7
and so how do i show it in terms of x+iy?

Thanks for all your help btw

Also, how do i begin this question -

- Jan 19th 2008, 05:04 PMThePerfectHacker
The first step is to find,

Which is,

Which is,

- Jan 19th 2008, 05:46 PMtopsquark
- Jan 19th 2008, 07:50 PMmr fantastic
- Jan 19th 2008, 08:11 PMtopsquark
- Jan 19th 2008, 08:35 PMThePerfectHacker
I remember when I first learned de Moivre's theorem I did not like solving the equation because of the setting up that is involved. But here is my perferred method which turns this problem into an automatic problem.

- Jan 20th 2008, 04:25 AMbrd_7
The two roots that i gained were