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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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