# Real and Complex Number Systems

• Dec 15th 2008, 06:20 AM
Conorsmom
Real and Complex Number Systems
Hi there....

This is what is given:

x = r(cos u + i sin u) and y = t(cos v + i sin v)

(1) Prove that the modulus of (xy) is the product of their moduli, showing each step.

(2) Prove that the amplitude of (xy) is the sum of their amplitudes, showing each step.

i need a starting point, desperately. This one is completely throwing me for a loop. Thanks!
• Dec 15th 2008, 06:29 AM
Greengoblin
Do you know of Eulers formula?

$e^{i\theta}=\cos{\theta}+i\sin{\theta}$
• Dec 15th 2008, 06:43 AM
Conorsmom
No, I do not....
• Dec 15th 2008, 06:48 AM
Greengoblin
Well applying it to your formulae:

$x=re^{iu},\quad y=te^{iv}$
• Dec 16th 2008, 02:18 AM
Quote:

(1) Prove that the modulus of (xy) is the product of their moduli, showing each step.
If you do not wish to resort to Euler's formula, you can multiply the terms out normally and then apply these formulas:
cos(u)cos(v)-sin(u)sin(v) = cos(u+v)
cos(u)sin(v)+sin(u)cos(v) = sin(u+v)

Quote:

(2) Prove that the amplitude of (xy) is the sum of their amplitudes, showing each step.
...
What is amplitude?