### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Introduction to Quadratic Equations and Complex Numbers

The equation is known as quadratic equation in one variable where i.e., we get the roots in real numbers.

Let’s take the equation , where , this is not a real number, i.e., for a quadratic equation where < , we can’t get a real roots for this. So we can take , is the imaginary number to find out the root of the equation .

Hence , in the quadratic equation we get two imaginary roots.

Complex Number:

The number which is of the form , where and are real numbers is defined to be a complex number.

We also take , where is the real part, denoted by and is the imaginary part denoted by .

The set consists of all the complex numbers is called a complex number set or set of complex numbers and denoted as .

For example,

,

Here

Two complex numbers and are equal iff and

Example:

If , where and are real numbers, then find the value of and .

Solution:

(Given)

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