Do you know of Eulers formula?
Hi there....
This is what is given:
x = r(cos u + i sin u) and y = t(cos v + i sin v)
I am being asked to:
(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!
If you do not wish to resort to Euler's formula, you can multiply the terms out normally and then apply these formulas:(1) Prove that the modulus of (xy) is the product of their moduli, showing each step.
cos(u)cos(v)-sin(u)sin(v) = cos(u+v)
cos(u)sin(v)+sin(u)cos(v) = sin(u+v)
...(2) Prove that the amplitude of (xy) is the sum of their amplitudes, showing each step.
What is amplitude?