
Complex Number
Calculate the real part, the imaginary part, and the absolute value of the following expression:
i * [(1+2i)(53i)+3i/(1+i)].
So I did the math out this way:
(1+2i)(53i)= 11+7i
(11+7i)+3i/(1+i)= (4+21i)/(1+i)
i * [(4+21i)/(1+i)] = (4i21)/(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.

(1+2i)(53i)= 11+7i is correct!
You should then rewrite 3i/(1+i)= (3i)(1i)/2 = (3+3i)/2
i[(11+7i)+ (3+3i)/2]=(7+11i)+(3+3i)/2 =(17/2)+(25/2)i

I really appreciate the help Plato. I was going to ask how the second part worked but I figured it out. You just multiply it by its conjugate.
Thanks anyway.

That really is an important point.
In general, we do not allow complex numbers written as 1/(a+bi).
In fact, the multiplicative inverse is, (a+bi)^(1) = (abi)/(a^2+b^2).
That is the conjugate divided by the absolute value squared.