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)|)))#