Which answer could be the result of two complex conjugates being multiplied together? (1 point)
16
9 - 9i
25 + 41i
20
9 - 9i
The correct answer could be (1) 16.
To find the result of two complex conjugates being multiplied together, we need to understand what complex conjugates are.
Complex conjugates are pairs of complex numbers that have the same real parts but opposite imaginary parts. If we have a complex number in the form a + bi, its complex conjugate would be a - bi.
To find the result of multiplying two complex conjugates together, we multiply their real parts and subtract the product of their imaginary parts.
Let's consider two complex conjugates: a + bi and a - bi.
Their product can be found using the FOIL method:
(a + bi)(a - bi) = a(a) + a(-bi) + bi(a) + bi(-bi)
= a^2 - abi + abi - bi^2
= a^2 - abi + abi + b^2i^2
Since i^2 equals -1, we can simplify further:
= a^2 + b^2(-1)
= a^2 - b^2
Based on this, the answer to the question, "Which answer could be the result of two complex conjugates being multiplied together?" is 16.