Common Misunderstandings About Complex Roots:

1. Do They Exist?
   A lot of people think that complex roots only show up when there are no real solutions to an equation. But here’s the truth: every polynomial with a degree of $n$ has exactly $n$ roots in the complex number system. This is part of the Fundamental Theorem of Algebra.

2. Imaginary Numbers Confusion:
   Some folks believe imaginary numbers are “less than” real numbers. This isn’t true! Complex numbers, which look like $a + bi$ (where $a$ and $b$ are real numbers and $i^2 = -1$), are just as important and real in their own way.

3. Not Just for Math Class:
   There’s a common idea that complex roots aren’t useful. But they actually come up in lots of areas, like engineering, especially in control theory, and in physics with wave functions. This shows they really matter in the real world.

4. Solving Equations:
   Many students ignore complex roots when they try to find the zeros of polynomials. However, about 30% of quadratic equations actually have complex solutions when the discriminant (a fancy term for a part of the equation) is negative.