Complex Numbers
- Author:
- Charles H. Lamb
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious and intuitive meaning.
The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero. The Fundamental Theorem of Algebra asserts that addition, subtraction, multiplication and division for real numbers can be carried over to complex numbers as long as division by zero is avoided.
ax^2+bx+c
The discriminant is the part of the quadratic formula under the square root. The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. It reveals what type of roots the equation has.