Hi I have 2 really really short questions and one medium length one I need help with!

1.)Does

equal to ?

2.)How do I, using complex number methods, deduce that cos(3x) = 4cos^3(x) - 3cos(x)?

3.)Does |a-bi| =a+bi?

Thank you so much!

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- December 10th 2012, 07:11 PMTutuComplex numbers
Hi I have 2 really really short questions and one medium length one I need help with!

1.)Does

equal to ?

2.)How do I, using complex number methods, deduce that cos(3x) = 4cos^3(x) - 3cos(x)?

3.)Does |a-bi| =a+bi?

Thank you so much! - December 10th 2012, 08:16 PMSorobanRe: Complex numbers
Hello, Tutu!

Quote:

2) How do I, using complex number methods, deduce that:

You should be familiar with this identity: .

For , we have: . .[1]

Expand the left side:

. .

n . . . . . . . . . . . .

Then [1] becomes: .

Equate real and imaginary components:

. . Hence: .

. . Hence: .

And we have the Triple-angle Identities for both sine and cosine.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Divide top and bottom by

Therefore: .