Complex Numbers and Quadratic Equations Class 11 Notes
Chapter 5 Complex Numbers and Quadratic Equations
NCERT Grade 11 Maths Chapter 5 Complex Numbers and Quadratic Equations: May be helpful for students preparing for the CBSE Grade 11. Experts prepare NCERT math notes for class 11 on Vidyakul following the latest CBSE guidelines.
Complex Numbers and Quadratic Equations is part of the 2021-2022 CBSE Semester 1 curriculum and covers many of the most important mathematical theorems and equations. This article provides CBSE Class 11 Math Chapter 5 notes in PDF format. Students can download the notes for free without registration.
MATHEMATICS NOTES CHAPTER- 5
Points to Remember
We have provided a few important points that are covered in NCERT Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations to help students in their exam preparations. Refer to the points below:
√-1 is an imaginary quantity and is denoted by i.
i2 = −1, i3 = −i, i4 = 1 and, i±n = i±k, n ∈ N where k is the remainder when n is divided by 4.
For any positive real number a, √−a = i√a.
If a, b are real numbers, then a number z = a + ib is called a complex number.
Real number a is known as the real part of z and b is known as its imaginary part. We write a = Re(z), b = lm(z).
A complex number z is purely real if lm(z) = 0 and z is purely imaginary if Re(z) = 0.
For any two complex numbers, z1 = a1 + ib1 and z2 = a2 + ib2.
Addition: z1 + z2 = (a1 + a2) + i(b1 + b2)
Subtraction: z1 − z2 = (a1 − a2) + i(b1 − b2)
Multiplication: z1z2 = (a1a2 − b1b2) + i(a1b2 + a2b1)
Topics and Sub-topics
Students can refer to the table below to check the important topics covered in NCERT Class 11 Math Chapter 5:
√-1 is an imaginary quantity and is denoted by i.
i2 = −1, i3 = −i, i4 = 1 and, i±n = i±k, n ∈ N where k is the remainder when n is divided by 4.
For any positive real number a, √−a = i√a.
If a, b are real numbers, then a number z = a + ib is called a complex number.
Real number a is known as the real part of z and b is known as its imaginary part. We write a = Re(z), b = lm(z).
A complex number z is purely real if lm(z) = 0 and z is purely imaginary if Re(z) = 0.
For any two complex numbers, z1 = a1 + ib1 and z2 = a2 + ib2.
Addition: z1 + z2 = (a1 + a2) + i(b1 + b2)
Subtraction: z1 − z2 = (a1 − a2) + i(b1 − b2)
Multiplication: z1z2 = (a1a2 − b1b2) + i(a1b2 + a2b1)
Learn more about this in Complex Numbers and Quadratic Equations Class 11 Notes pdf.
Download this solution for FREE Download this PDF
Download Vidyakul App for more videos, PDF's and Free video lectures.
