Imaginary multiplication with answer to be in polar (variables)

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?

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