If x1 + iy1 is an element of C and has an absolute value r1 and argument phi1, and

x2 + iy2 is an element of C and has absolute value r2 and argument phi2, then

the product (x1 + iy1)(x2 + iy2) has absolute value r1r2 and argument (one among many) phi1 + phi2

where C is the set of complex numbers. Any help would be appreciated for this proof!