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It comes from Euler's formula - <a href="http://en.wikipedia.org/wiki/Euler's_formula" rel="ugc">http://en.wikipedia.org/wiki/Euler's_formula</a><br />
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e^(i theta) == cos(theta) + i sin(theta)<br />
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It comes from Euler's formula - http://en.wikipedia.org/wiki/Euler's_formula [http://en.wikipedia.org/wiki/Euler's_formula]

e^(i theta) == cos(theta) + i sin(theta)



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I'm working with complex numbers and reading through a solution, <br />
<br />
It begins like this - In polar form, -27 = 27 (cos(pi) + i sin(pi))<br />
<br />
I get that, but then it says<br />
<br />
If z = r(cos(theta)+i sin(theta), then the equation z^3 = -27 can be written as<br />
<br />
r^3(cos(3(theta)+i.sin(3(t<wbr />heta)) = 27(cos(pi) + i sin(pi))<br />
<br />
I don't see where the left hand side came from??<br />
<br />
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I'm working with complex numbers and reading through a solution, 

It begins like this - In polar form, -27 = 27 (cos(pi) + i sin(pi))

I get that, but then it says

If z = r(cos(theta)+i sin(theta), then the equation z^3 = -27 can be written as

r^3(cos(3(theta)+i.sin(3(theta)) = 27(cos(pi) + i sin(pi))

I don't see where the left hand side came from??




Why can z^3 = -27 be written as r^3(cos(3(theta)+i.sin(3(theta))?

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