In need proof of all justifications on a moduli equation?
x=r(cos u + i sin u)
y=t(cos v + i sin v)
So, you simply multiply by by expanding the brackets, but leave the and outside:
, by re-arranging the order of the terms, and using (1)
, using (2) and (3)
, where and
And this is a complex number whose modulus is , and amplitude , where product of the moduli of and , and sum of their amplitudes.