# Math Help - Complex Number

1. ## Complex Number

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.

2. (1+2i)(5-3i)= 11+7i is correct!
You should then rewrite 3i/(1+i)= (3i)(1-i)/2 = (3+3i)/2
i[(11+7i)+ (3+3i)/2]=(-7+11i)+(-3+3i)/2 =(-17/2)+(25/2)i

3. 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.

4. 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) = (a-bi)/(a^2+b^2).
That is the conjugate divided by the absolute value squared.