Question

What is the conjugate of `7+2i`?

Answer 1

7 - 2i

Explanation:

If `a + color(blue)" bi " " is a complex number "`

then `a - color(red) "bi " " is the conjugate"`

note that when you multiply a complex number by it's conjugate .

`(a + bi)(a - bi) = a^2 + abi - abi + bi^2 = a^2 - b^2`

the result is a real number. This is a useful result.

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

so 4-5i has conjugate 4 + 5i.

The real term remains unchanged but the imaginary term is the negative of what it was.