purplesoup
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Why can z^3 = -27 be written as r^3(cos(3(theta)+i.sin(3(theta))?
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(t heta)) = 27(cos(pi) + i sin(pi))
I don't see where the left hand side came from??
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(t
I don't see where the left hand side came from??
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SOLUTION
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ASKER
That's great - thanks!
e^(i theta) == cos(theta) + i sin(theta)