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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Find the four fourth roots of .
Oh ok, And how do i go about starting that?
Originally Posted by brd_7 Oh ok, And how do i go about starting that? I favor putting the complex number into polar form: Then go from there. -Dan
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?
Yes it is correct if this is what you mean.
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 -
The first step is to find, Which is, Which is,
Originally Posted by brd_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 - Tsk! New questions go in new threads. I would expand: which is a biquadratic and easy to solve. -Dan
Originally Posted by topsquark I favor putting the complex number into polar form: Then go from there. -Dan I have a preference cutting straight to the chase and using .
Originally Posted by mr fantastic I have a preference cutting straight to the chase and using . Well... If I want to do it the hard way, then let me! -Dan
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.
The two roots that i gained were
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