In 3-5 sentences, explain why complex solutions come in conjugate pairs. Consider the structure of the quadratic formula in your response.

Answer 1

Complex solutions come in conjugate pairs because the structure of the quadratic formula involves the discriminant, which is the term inside the square root. If the discriminant is negative, it implies that the quadratic equation does not have real solutions. Instead, it has two complex solutions of the form (a + bi) and (a - bi), where a and b are real numbers. This is why complex solutions come in conjugate pairs with the same real part and opposite imaginary parts.