NCERT Solutions for Class 11 Maths Chapter 4
Chapter 4.1: Introduction to Complex Numbers
- Imaginary Unit (i): Defined as √(-1).
- Complex Number: A number of the form a + bi, where a and b are real numbers and i is the imaginary unit.
- Real and Imaginary Parts: The real part of a + bi is a, and the imaginary part is b.
- Equality of Complex Numbers: Two complex numbers are equal if their real and imaginary parts are equal.
Chapter 4.2: Algebraic Operations with Complex Numbers
- Addition and Subtraction: Add or subtract the corresponding real and imaginary parts.
- Multiplication
- Division
Chapter 4.3: Polar Representation of a Complex Number
- Modulus of a Complex Number: The distance of the complex number from the origin in the complex plane.
- Argument of a Complex Number
- Polar Form: A complex number can be represented as r(cos θ + i sin θ), where r is the modulus and θ is the argument.
Chapter 4.4: Quadratic Equations
- Quadratic Equation: An equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
- Roots of a Quadratic Equation: The values of x that satisfy the equation.
- Discriminant (Δ): Δ = b² – 4ac
- If Δ > 0, the equation has two distinct real roots.
- If Δ = 0, the equation has one real root (repeated).
- If Δ < 0, the equation has no real roots (but two complex conjugate roots).
- Quadratic Formula: x = (-b ± √Δ) / (2a)
Key Concepts:
- Complex numbers and their operations
- Polar representation of complex numbers
- Quadratic equations, their roots, and the discriminant
- The relationship between quadratic equations and complex numbers
NCERT Solutions for Class 11 Maths Chapter 4
Exercise 4.1
Express each of the complex number given in the Exercises 1 to 10 in the form
a + ib.
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2.
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3. i-39
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4. 3(7 + i7) + i (7 + i7)
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5. (1 – i) – ( –1 + i6)
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(1 – i) – ( –1 + i6) = 1 – i + 1 – 6i
= 2 – 7i
6.
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7.
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8. (1-i)4
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9.
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10.
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Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13.
11. 4 – 3i
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12.
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13. – i
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14. Express the following expression in the form of a + ib :
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NCERT Solutions for Class 11 Maths Chapter 4
FAQ’s
What is Chapter 4 in Class 11 Maths about?
Chapter 4 explains Complex Numbers and Quadratic Equations, covering concepts like imaginary numbers, algebra of complex numbers, and solving quadratic equations.
Why are complex numbers important in Class 11 Maths?
Complex numbers help solve equations that have no real solutions. They form the foundation for higher-level maths, engineering, and physics.
What topics are included in Complex Numbers and Quadratic Equations?
The chapter includes imaginary units, complex number operations, polar form, quadratic formula, discriminant, and nature of roots.
How do NCERT solutions help in studying Chapter 4?
NCERT solutions provide step-by-step explanations, making it easier to understand tricky concepts and practice exam-based questions.
Where can I find reliable study material for Class 11 Maths Chapter 4?
You can find accurate and free study material, notes, and NCERT solutions for Chapter 4 on trusted educational websites and learning platforms.
