- #1
Valhalla
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I just bombed a quiz because it was 2 questions and this was one of them:
Find all three complex roots of the following equation (give answers in polar and rectangular form)
[tex]z^3+8=0[/tex]
Looks easy enough,
[tex] z=2e^{-i\frac{\theta}{3}} [/tex]
This is where I think I completely realized I wasn't sure what I was doing. My roommate suggested I look for the roots of unity which I know that:
[tex]r^n(cos(n\theta)+isin(n\theta))=1+i*0[/tex]
so if I want to consider mine it should be:
[tex]8^{1/3}(cos(\frac{\theta}{3})+isin(\frac{\theta}{3})=-8 [/tex]
so then
[tex]\theta=\frac{k2\pi}{3}[/tex]
is this the right track?
Find all three complex roots of the following equation (give answers in polar and rectangular form)
[tex]z^3+8=0[/tex]
Looks easy enough,
[tex] z=2e^{-i\frac{\theta}{3}} [/tex]
This is where I think I completely realized I wasn't sure what I was doing. My roommate suggested I look for the roots of unity which I know that:
[tex]r^n(cos(n\theta)+isin(n\theta))=1+i*0[/tex]
so if I want to consider mine it should be:
[tex]8^{1/3}(cos(\frac{\theta}{3})+isin(\frac{\theta}{3})=-8 [/tex]
so then
[tex]\theta=\frac{k2\pi}{3}[/tex]
is this the right track?
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