# Euler's Theorem Converting from Trignometric to Exponential Form

r(cos u + i sin u)

t(cos v + i sin v)

How do I convert these into exponential form using Euler's Theorem?

tiny-tim
Homework Helper
Welcome to PF!

r(cos u + i sin u)

t(cos v + i sin v)

How do I convert these into exponential form using Euler's Theorem?

Hi jaylwood! Welcome to PF!

cos u + i sin u = eiu

(I don't understand why you're not recognising that? )

okay here is the problem i have. Given x = r(cos u + i sin u) and y = t(cos v + i sin v)
Prove that the amplitude of (xy) is the sum of their amplitudes. I don't understand where to go with it.

tiny-tim
Homework Helper
okay here is the problem i have. Given x = r(cos u + i sin u) and y = t(cos v + i sin v)
Prove that the amplitude of (xy) is the sum of their amplitudes. I don't understand where to go with it.

ah … so that's the problem!

ok … x = r eiu, y = t eiv

so multiply them, and you get xy = … ?

rt eiu eiv What do i do to simplify that? Or reconvert it back to trignometric form?

tiny-tim
Homework Helper
rt eiu eiv What do i do to simplify that?

oh come on …

eiu eiv = … ?

ei(u+v)

tiny-tim
Homework Helper
amplitude …

ei(u+v)

(just got up … :zzz:)

That's right!

So the amplitude of xy is … ?

u+v ? but what happens to the rt?

Last edited:
tiny-tim
Homework Helper
u+v ?

Yes!

(it's that easy )

Any other problems?

what happens to the rt?

tiny-tim
Homework Helper
what happens to the rt?

They're just ordinary numbers.

Treat them as usual …

xy = rt ei(u+v)

So what would be my final answer?

tiny-tim