Complex solutions come in conjugate pairs because of the way equations and their roots behave. When we use the quadratic formula, which is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), the part under the square root, called the discriminant (\( b^2 - 4ac \)), can be negative. This means we'll get a square root of a negative number, which is where imaginary numbers come in. If one solution is \( a + bi \) (where \( i \) is the imaginary unit), the other solution will be \( a - bi \) because the plus and minus in the formula give us both the positive and negative parts, making sure both complex solutions are present.
n 3-5 sentences, explain why complex solutions come in conjugate pairs. You can use the quadratic formula to assist with your answer. explain in a easy way like a highschooler wrote it
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