Calculate the real part, the imaginary part, and the absolute value of the following expression:

i * [(1+2i)(5-3i)+3i/(1+i)].

So I did the math out this way:

(1+2i)(5-3i)= 11+7i

(11+7i)+3i/(1+i)= (4+21i)/(1+i)

i * [(4+21i)/(1+i)] = (4i-21)/(1+i)

Is this correct and what do you call the imaginary part and the real part if a denominator exists with an imaginary i?

Thanks for any help.