Imaginary multiplication with answer to be in polar (variables)

1. Mar 5, 2006

sportsguy3675

I have to find (a+bi)(c+di) in polar form given that b,c,d>0 and a<0.

So I convert each one to polar first.

$$( (a+b)cis(\arctan(-b/a) + \pi) ) ( (c+d)cis(\arctan(d/c)) )$$

That's as far as I got. Little help please?

Last edited: Mar 5, 2006
2. Mar 5, 2006

mr bob

Multiply the numbers out first. Then you will have just one complex number. Then just find the modulus and argument using pythagoras and arctan like you mentioned.

3. Mar 5, 2006

sportsguy3675

That would give -(ac) -(adi) +(bci) -(bd)?

But how do I find a modulus and argument with that?