Question

How do you simplify `(5 + 2i)(5 - 2i)` and write in a+bi form?

Answer 1

`29`

Explanation:

Given,

`(color(red)5color(white)(i)color(blue)(+2i))(color(darkorange)5color(white)(i)color(teal)(-2i))`

Use the F.O.I.L. (first, outside, inside, last) method to expand the brackets.

`=color(red)5(color(darkorange)5)color(white)(i)color(red)(+5)(color(teal)(-2i))color(white)(i)color(blue)(+2i)(color(darkorange)5)color(white)(i)color(blue)(+2i)(color(teal)(-2i))`

Simplify.

`=25-10i+10i-4i^2`

`=25-4i^2`

Since `i^2=-1`, the expression simplifies to,

`=25-4(-1)`

`=25+4`

`=color(green)(|bar(ul(color(white)(a/a)color(black)(29)color(white)(a/a)|)))`