In 3-5 sentences, explain why complex solutions come in conjugate pairs. Consider the structure of the quadratic formula in
your response.
1 answer
Complex solutions come in conjugate pairs because the quadratic formula involves taking the square root of the discriminant, which can be negative in the case of complex solutions. The square root of a negative number results in an imaginary number, and since the quadratic formula includes both a positive and negative square root, it yields two complex solutions that are conjugates of each other. This is due to the fact that the sum and product of conjugate pairs of complex numbers are always real.