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# NCERT Solutions for Class 11 Maths Chapter 5 - Complex Numbers and Quadratic Equations

Chapter number five "Complex Numbers and Quadratic Equations" decode the importance of complex numbers, mainly -1, which is prompted because of the failure to solve some of the quadratic equations. The chapter also discusses the algebraic properties of complex numbers, what the argand plane is, and how the polar representation of complex numbers is done.

Apart from this, some more topics are included in this chapter: quadratic equation solutions in the complex number system with real coefficients, statements about the fundamental theorem of algebra, and how to find the square root of a complex number. The topics introduced in this chapter are mentioned below.

• Complex Numbers

When no real solutions can be found for a quadratic equation, it means that the solutions in respect of such equations involve complex numbers. This part of the chapter discusses the definition of complex numbers along with appropriate examples. Complex numbers have imaginary and real parts that are also explained under this section.

• Algebra of Complex Numbers

Here, addition, subtraction, multiplication, and division of two complex numbers; the square root of a real number, which is negative; and the application of the general BODMAS rules on complex numbers are taught.

• The Modulus and Conjugate of Complex Numbers

Under this portion, the above topic has been explained in detail using solved examples.

• Polar Representation and Argand Plane

How the ordered pairs for the specific complex numbers are written, how the ordered pairs regarding complex numbers are polarly represented, and the meaning of the argand plane or complex plane are discussed.