Question

find the product of the given complex number and its conjugate. write the answer in the form \\(a + bi\\).

\\6 + 2i\\

the product of \\(6 + 2i\\) and its conjugate is \\(\square\\)
(simplify your answer. use integers or fractions for any numbers in the expression. type your answer in the form \\(a + bi\\).)

Explanation:

Find the complex conjugate

Using the Complex Numbers knowledge point
The conjugate of \(6 + 2i\) is \(6 - 2i\).

Set up the product

Using the Complex Numbers knowledge point

$$ (6 + 2i)(6 - 2i) $$

Expand the expression

Using the Complex Numbers knowledge point

$$ 6^2 - (2i)^2 = 36 - 4i^2 $$

Simplify using the imaginary unit

Using the Imaginary Unit knowledge point

$$ 36 - 4(-1) = 36 + 4 = 40 $$

Write in standard form

Using the Complex Numbers knowledge point

$$ 40 + 0i $$

Answer:

The product of \(6 + 2i\) and its conjugate is <blank>\(40 + 0i\)</blank>