complex numbers question (1 Viewer)

[.ben]

hi

anyone know how to do this proof question?

(cosθ+isinθ)/(cosØ+isinØ)=cos(θ-Ø)+isin(θ-Ø)

any help would be appreciated thanks.

 

[lucifel]

treat the cos and sins as real and unreal part and rationalise denominator. then you gather up certain terms, and you should have that formula. I'd write out the actual working, but that's laborioous to type and read.

 

[FinalFantasy]

hi

anyone know how to do this proof question?

(cosθ+isinθ)/(cosØ+isinØ)=cos(θ-Ø)+isin(θ-Ø)

any help would be appreciated thanks.

hihi!
(cosθ+isinθ)/(cosØ+isinØ)
=(cosθ+isinθ)/(cosØ+isinØ) * (cosØ-isinØ)\(cosØ-isinØ)
=(cosθcosØ-isinØcosθ+isinθcosØ+sinθsinØ)\(cos²Ø+sin²Ø)
=(cosθcosØ-isinØcosθ+isinθcosØ+sinθsinØ)
=cos(θ-Ø)+isin(θ-Ø)

 

[acmilan]

If you know that e^iθ = cosθ+isinθ,

then
(cosθ+isinθ)/(cosØ+isinØ)
= e^iθ/e^iØ
= e^i(θ-Ø)
= cos(θ-Ø)+isin(θ-Ø)

Very quickly done

 

[.ben]

wow thanks for the quick reply guys I get it now thanks!