Question

What does `(1+i)*(6-2i)-4i` equal?

Answer 1

`(1+i) * (6-2i) = 8`

Explanation:

First evaluate `(color(red)(1+i)) * (color(blue)(6-2i))`
This can be done in various ways: FOIL, or using the distributive property, or tabular multiplication (below)
`color(white)("XXX"){: (xx, color(red)(1),color(red)(+i)), (color(blue)(6),color(orange)(6),color(green)(+6i)), (color(blue)(-2i),color(green)(-2i),color(orange)(+2)), (,"-----","-----"), (,color(orange)(8),color(green)(+4i)) :}`

If `color(cyan)((1+i) * (6-2i)) = color(cyan)(8+4i)`
then `color(cyan)((1+i) * (6-2))-4i = color(cyan)(8+4i)-4i = 8`