Write the complex conjugate of the complex number.

Question

2 + 3i

Conjugate:

Multiply the number by its complex conjugate. (Simplify your answer completely.)

=

Answer 1

(2 + 3i)(2 - 3i) = 4 - 9i²

Since i = the square root of -1, i² = -1.

4 - 9(-1) = 4 + 9 = 13

Answer 2

Conjugate of a+bi is a-bi (just negate the imaginary part)

(a+bi)(a-bi) = a² - abi + abi - b²i² = a²+b² (the imaginary part cancels and you are left with a pure real)