What is the product of a complex conjugated?

The product of complex conjugates is a difference of two squares it is always a real number.

The product a complex conjugates may be written in standard form as a + bi where neither a nor b is zero.

The product of complex conjugates is a sum of two squares and is always a real number.

The product of complex conjugates is the same as the product of opposites.

(a+bi)(a-bi) = a^2 - (bi)^2 = a^2 - b^2 i^2

But i^2 = -1, so that makes it a^2 + b^2

The answer is A: the product is the difference of 2 squares and always a real number.

***Do NOT let the words "Complex Number" freak you out.***
It's still the same as any real numbers used before with just the addition of the imaginary unit of (i). When you have (i)^2 then it becomes a -1 in place of that square. So an example would be: (2+3i)(2-3i)=2(2+3i) + -3i(2+3i) with the "distributive property" of algebra/mathematics. <JUST TAKE THE 2nd PART AND PUT IT THROUGH THE 1st>
Then do the math operation like you've always done to get: (4+6i)+(-6i-9i^2) = (4+6i)+(-6i-9(-1))
combine like terms, simplify if possible, then write in standard form: the +6i & -6i cancel each other out, the i^2 becomes a -1 to be multiplied into the -9 to = +9 then write correctly after simplifying: 4+9=13 so 13 is the answer
***hope that helps***

To find the product of complex conjugates, follow these steps:

1. Write the original complex number in the form a + bi, where a and b are real numbers and i is the imaginary unit.
2. Replace the imaginary part (bi) with its conjugate form (-bi).
3. Multiply the two complex numbers, treating them as binomials.

For example, let's say we have the complex number (3 + 2i) and its conjugate (-3 - 2i). The product of these complex conjugates can be found as follows:

(3 + 2i)(-3 - 2i)

Using the distributive property and FOIL (First, Outer, Inner, Last) method, multiply each term:

= 3(-3) + 3(-2i) + 2i(-3) + 2i(-2i)
= -9 - 6i - 6i - 4i^2
= -9 - 6i - 6i - 4(-1) (since i^2 = -1)
= -9 - 12i + 4
= -5 - 12i

The result of the product of these complex conjugates is -5 - 12i, which is a complex number of the form a + bi, where a and b are real numbers.

how does this help im still confused