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

1 Answer
May 17, 2016

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)|)))