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!
Hello, Tutu!
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: .