Question

How do you simplify `(-2-i)^2`?

Answer 1

`(-2-i)^2=3+4i`

Explanation:

In general
`color(white)("XXX")(color(red)a+color(blue)b)^2 = color(red)a^2+2color(red)acolor(blue)b+color(blue)b^2`

`(-2-i)^2 = (color(red)(""(-2))+color(blue)(""(-i)))^2`

Substituting `color(red)a=color(red)(""(-2))` and `color(blue)b=color(blue)(""(-i))`
We have
`color(white)("XXX")color(red)(""(-2))^2+2 * color(red)(""(-2)) * color(blue)(""(-i))+color(blue)(""(-i))^2`

`color(white)("XXX")= 4 + 4i -1`

`color(white)("XXX")=3+4i`