Question

Operations with complex numbers

What is the product of complex conjugates?

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

The product of 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 difference of two squares and is always a real number.

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

I believe it is D, but i am not very sure

Answer 1

since i^2 = -1,
(a+bi)(a-bi) = a^2 - (bi)^2 = a^2 - b^2 i^2= a^2 + b^2
so, what do you think?

Answer 2

I am brand new to this so honestly i dont know. Is it c?

Answer 3

no. remember that a and b are real numbers.
So, the sum a^2+b^2 is always real and positive.
You may be new to complex numbers, but you've been working with real numbers for a while now ...