• Support PF! Buy your school textbooks, materials and every day products Here!

Not certain about Complex Number, Polar Form Question

  • Thread starter linuxux
  • Start date
  • #1
133
0

Homework Statement


The question:
a)Solve the equation [tex]z^{3}=4\sqrt{2}-4\sqrt{2}i.[/tex].
b)Express the answer in polar form.


The Attempt at a Solution



Here's what i got:

[tex]r=\sqrt{\left(4\sqrt{2}\right)^{2}+\left(-4\sqrt{2}\right)^{2}}=8[/tex]
[tex]\tan^{-1}\left(\frac{-4\sqrt{2}}{4\sqrt{2}}\right)=-45^{o}[/tex]
[tex]z^{3}=8^{3}cis\left(-45\cdot3\right)[/tex]
[tex]z^{3}=512\left(cos\frac{5\pi}{4}-i\sin\frac{5\pi}{4}\right)[/tex]
[tex]z^{3}=512\left(\frac{-\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i\right)[/tex]
[tex]=-256\sqrt{2}+256\sqrt{2}i\right)[/tex]

im not sure if this is right, im supposed to graph this, and with these kinds of numbers, i figure i went wrong somewhere, i have no idea what they mean by "solve" and how or if this "solves" anything other than the fact that it ends with an equal sign, so if someone can check it for me id appreciate it, thanks."
 
Last edited:

Answers and Replies

  • #2
mjsd
Homework Helper
726
3
i think you are solving for z, so you should have
[tex]z^{3}=4\sqrt{2}-4\sqrt{2}i=8 cis\left(-45\right)[/tex]
and then cube root both sides....
hint: should get 3 roots
 
  • #3
133
0
oh, so i went too far, now i see what im supposed to be solving, thanks.
 

Related Threads for: Not certain about Complex Number, Polar Form Question

  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
14
Views
2K
  • Last Post
Replies
2
Views
541
  • Last Post
Replies
3
Views
768
Replies
4
Views
1K
Replies
2
Views
6K
Replies
7
Views
1K
Replies
4
Views
6K
Top