Question

How to multiply (x - (3 + 2i)) times (x - (x - 2i)) ?

Answer 1

\[(x - (3 + 2i))(x - (3 - 2i))\]

Answer 2

You can start with FOIL \((a-B)(a-b)=a^2-aB-ab-Bb\)
a=x, B=3+2i, b=3-2i
then you distribute aB as x(3+2i), and ab as x(3-2i).
Finally, \(bB = (3+2i)(3-2i)\) can be expanded to the difference of two squares, namely
\((3+2i)(3-2i)=3^2-(2i)^2.\)

Recall: \((2i)^2=2^2i^2\)

Answer 3

* \((a-B)(a-b)=a^2-aB-ab\color{red}{+}Bb\)

Answer 4

Thanks - very helpful. I'll go through a few similar problems and see if I hit any walls.