Using eulers formula show that sin3x = 3sinx - 4sin^3x

How do I do that?

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- May 2nd 2012, 05:43 AMqwerty31complex numbers eulers formula
Using eulers formula show that sin3x = 3sinx - 4sin^3x

How do I do that? - May 2nd 2012, 05:53 AMProve ItRe: complex numbers eulers formula
No need for Euler's formula.

You know that by the Binomial Theorem, and by DeMoivre's Theorem.

Try applying each of these to , setting them equal, and equating real and imaginary parts :) - May 2nd 2012, 05:58 AMqwerty31Re: complex numbers eulers formula
- May 2nd 2012, 06:12 AMProve ItRe: complex numbers eulers formula
Hmm, well let's see...

Q.E.D. - May 2nd 2012, 06:14 AMqwerty31Re: complex numbers eulers formula
- May 2nd 2012, 06:15 AMProve ItRe: complex numbers eulers formula
- May 2nd 2012, 06:19 AMqwerty31Re: complex numbers eulers formula
- May 2nd 2012, 06:20 AMProve ItRe: complex numbers eulers formula
- May 2nd 2012, 06:27 AMqwerty31Re: complex numbers eulers formula
thank you so much :) one more quick question, when solving square roots (or cube roots etc) of complex numbers, is there any specific patterns of what values of k to choose after equating the angles? I know for square roots the values of k taken are usually 0 and 1, but for cube roots some people take 0, 1, 2 and others take 0, 1, -1?

- May 2nd 2012, 07:01 AMProve ItRe: complex numbers eulers formula