Complex Number Calculation: Real, Imaginary, and Absolute Value Explanation

[JaysFan31]

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.

 

[JaysFan31]

Yeah I figured it out. You just multiply it by its conjugate earlier in the process.