Question

How do you simplify `(2+7i)(2-7i)`?

Answer 1

53

Explanation:

distribute the brackets using FOIL

`(2+7i)(2-7i) = 4 -14i+14i -49i^2`

[ remember that `i^2 =(sqrt-1)^2 = -1`]

so `4 - 14i + 14i -49i^2 = 4 - 14i + 14i + 49`

= 53

(Worth noting here that when you multiply a complex number by it's conjugate you obtain a real number.)

ie. If a + bi is a complex number then a - bi is it's conjugate.

and (a+ bi)(a-bi) `= a^2 + b^2color(black)(" a real number")`