Imaginary multiplication with answer to be in polar (variables)

[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?

 

[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.

 

[sportsguy3675]

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

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