Complex Roots of a Quadratic equation
A quadratic equation is a polynomial equation where the highest exponent of the variable is 2. It is represented as ax2 + bx + c = 0. This equation has imaginary or complex roots when the discriminant (D = b2-4ac) is less than zero.
Complex roots of a quadratic equation always occur in pairs, i.e. if α and β are complex roots of a quadratic equation, then they are of the form (c + id) and (c – id), where ‘c’ and ‘d’ are real numbers and ‘i’ denotes the square root of -1 called as iota.
Complex Roots
Complex roots in mathematics typically arises when solving polynomial equations that don’t have real solutions. A complex number is composed of a real part and an imaginary part and is generally written in the form a+bi where a and b are real numbers, and i is the imaginary unit with the property i2=−1.
Complex Roots
Complex roots refer to the solutions of equations that take the form of complex numbers, occurring when the discriminant of a quadratic equation is less than zero. These roots, which are also known as imaginary roots, are expressed in the format α = a + ib and β = c + id, where each root comprises a real component and an imaginary component.
In this article, we will learn about complex roots, arithmetic operations on complex roots, methods to find complex roots of a quadratic equation, and some practice problems based on them.
Table of Content
- Complex Roots
- Complex Roots Definition
- Mathematically
- Complex Roots of a Quadratic equation
- Operations on Complex Roots
- Addition Of Complex Roots
- Subtraction of Complex Roots
- Multiplication of Complex Roots
- Division Of Complex Roots
- Properties Of Complex Roots
- Polar Representation of Complex Roots
- How to Find Complex Roots of a Quadratic Equation?
- Complex Roots Examples
- Practice Problems on Complex Roots