Is r,theta Equivalent to cos(theta)+isin(theta) in Complex Numbers?

[Mrencko]

Homework Statement

well this is not exactly a homework, i had an argument whith my teacher about my grade in a test, because i put a complex number in the form of R,theta and she claims that the form was costheta+isentheta, and i know that but i need to prove in a book that r,theta=costheta+isentheta[/B]2. The attempt at a solution
she ditnt request, a solution or demostration just if someone knows a book about the fact, please help me, the matter is from a very good grade to a failure grade so this is important, thank you
i truly believe i am right but the teacher want to screw me really bad and asked for evidence in a book

 

[FactChecker]

The correct equality would be r⋅e^iθ = r⋅(cos(θ)+i sin(θ)).
I'm not sure exactly what you were asked for on the test.

 

[Mark44]

Homework Statement

well this is not exactly a homework, i had an argument whith my teacher about my grade in a test, because i put a complex number in the form of R,theta and she claims that the form was costheta+isentheta, and i know that but i need to prove in a book that r,theta=costheta+isentheta[/B]

i truly believe i am right but the teacher want to screw me really bad and asked for evidence in a book

r,theta=costheta+isentheta makes no sense. As @FactChecker already said, the correct identity is $re^{i\theta} = r(\cos(\theta) + i\sin(\theta))$