# Product of Complex Numbers proof

• December 8th 2010, 02:45 PM
jstarks44444
Product of Complex Numbers proof
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!
• December 8th 2010, 02:59 PM
pickslides
First thing to do is expand $(x_1 + iy_1)(x_2 + iy_2)$ , then re-write the result as $x+yi$ and find $r$ and $\phi$
• December 8th 2010, 03:31 PM
TheCoffeeMachine
$(x_1 + iy_1)(x_2 + iy_2) = r_{1}e^{i\varphi_{1}}r_{2}e^{i\varphi_{2}} = r_{1}r_{2}e^{i(\varphi_{1}+\varphi_{2})$.