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

##### 1 Answer

Mar 2, 2016

#### Answer:

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.