Are there any numbers above or below the number line? Is there a way to represent these numbers that are not on the number line? Does every equation have a solution? In this chapter on complex numbers, we will answer all of these questions and develop a new and powerful branch of Mathematics – the imaginary numbers or the Complex numbers.

First of all, we will see what complex numbers are. After that, we will learn about the algebra of complex numbers also known as the complex analysis. Let’s begin!

- Basics of Complex Numbers
- Operations on Complex Numbers
- Modulus and Conjugate of a Complex Number
- Argand Plane and Polar Representation
- Complex Quadratic Equations

**FAQs on Complex Numbers and Quadratic Equations**

**Question 1: What is a complex number?**

**Answer:** On the basis of the concept of a real number, a complex number is a number of the form a + bi. Here a and b are real numbers and ‘i’ is an indeterminate satisfying i^{2} = -1. For instance, 4 + 5i is a complex number.

**Question 2: Is 1 a complex number?**

**Answer:** Complex number refers to all those numbers that we can express in the form of a + bi, where a and b are real number and ‘i’ is a solution of the equation x^{2} = -1. Since no real number satisfies this equation, ‘i’ is called an imaginary number.

**Question 3: Do the complex number really exists?**

**Answer:** They are not real numbers also they can’t be quantified on a number line. They are real in the sense that they exist in and used in Math. Moreover, we use them in electricity as well as quadratic equations.

**Question 4: Are complex numbers irrational?**

**Answer:** Those mathematicians that are especially engaged in conducting research on the transcendental number for them every complex number or imaginary numbers with a non-zero imaginary part are irrational. In simple words, every non-zero number is irrational.