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FP2 Complex Numbers - HELP

I've been set this ridiculous set of questions for homework (either that or I'm just dim). Can anyone shed light on this one?

By considering (cosθ +isinθ)^4 express tan4θ in terms of tanθ.

I don't even know where to begin. Any thoughts? Thanks. :smile:
Reply 1
Avatar for f1mad
f1mad
13
Okay you should know that tan4 theta= sin4theta/cos4theta. You need to work out the individual expansions of sin4theta and cos4theta by considering the real and imaginary parts of the expansion of (cos theta+isin theta)^4

I.e cos 4theta= Real parts of (cos theta+isin theta)^4
Reply 2
Avatar for Exitthefall
Exitthefall
OP
I got the tanθ = sinθ / cosθ but I couldn't even start to think what to do next. :tongue:

I think this is just a case of tedious expanding? Uh oh.

Thanks for your help. :smile:
Reply 3
Avatar for ElMoro
ElMoro
18
Just to add to f1mad's post, cos 4theta= Real parts of (cos theta+isin theta)^4 because of De Moivre's Theorem

(cos⁡x+isin⁡x)n=cos⁡(nx)+isin⁡(nx)(\cos x + i \sin x)^n = \cos (nx) + i \sin (nx)

Original post by Exitthefall
I think this is just a case of tedious expanding? Uh oh.


Remember you can you use binomial expansion - it's not too bad :wink2:
(edited 12 years ago)

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