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2.Complex Numbers – Basics & Operations
Class 11 • Mathematics • NCERT
Complex Numbers – Basics & Operations
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This lesson introduces complex numbers as per NCERT Class 11. Students learn the imaginary unit, standard form of complex numbers, and basic operations such as addition, subtraction, and multiplication.
Lesson Objectives
- Understand the need for complex numbers.
- Define the imaginary unit i.
- Write complex numbers in standard form.
- Perform basic operations on complex numbers.
1. Introduction to Complex Numbers
Complex numbers are introduced to solve equations like x² + 1 = 0, which have no real solutions.
A complex number is of the form a + ib, where a, b ∈ ℝ.
2. Imaginary Unit
The imaginary unit i is defined as:
i² = −1
3. Equality of Complex Numbers
Two complex numbers are equal if their real parts and imaginary parts are equal.
If a + ib = c + id, then a = c and b = d
4. Operations on Complex Numbers
Addition:
(a + ib) + (c + id) = (a + c) + i(b + d)
(a + ib) + (c + id) = (a + c) + i(b + d)
Subtraction:
(a + ib) − (c + id) = (a − c) + i(b − d)
Multiplication:
(a + ib)(c + id) = (ac − bd) + i(ad + bc)
Practice Questions (NCERT)
- Define a complex number.
- What is the value of i²?
- Write the standard form of a complex number.
- When are two complex numbers equal?
- Find (2 + 3i) + (1 − i).
- Find (4 + i) − (2 + 3i).
- Multiply (1 + i)(1 − i).
- What is the real part of 5 − 2i?
- What is the imaginary part of 3 + 7i?
- Is every real number a complex number?
✅ Show Answer Key
- A number of the form a + ib.
- −1
- a + ib
- When real and imaginary parts are equal.
- 3 + 2i
- 2 − 2i
- 2
- 5
- 7
- Yes
© Aviate Learning – Complex Numbers (NCERT Class 11)