How do you simplify (5 + 2i)(5 - 2i)(5+2i)(5−2i) and write in a+bi form?
1 Answer
May 17, 2016
Explanation:
Given,
(color(red)5color(white)(i)color(blue)(+2i))(color(darkorange)5color(white)(i)color(teal)(-2i))(5i+2i)(5i−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))=5(5)i+5(−2i)i+2i(5)i+2i(−2i)
Simplify.
=25-10i+10i-4i^2=25−10i+10i−4i2
=25-4i^2=25−4i2
Since
=25-4(-1)=25−4(−1)
=25+4=25+4
=color(green)(|bar(ul(color(white)(a/a)color(black)(29)color(white)(a/a)|)))
