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Introduction to Complex Numbers Video Lecture | Mathematics (Maths) Class 11 - Commerce

85 videos|243 docs|99 tests

Timeline

00:03 Real numbers
00:16 Rational numbers
00:23 Irrational numbers
01:20 Roots of a quadratic equations
02:51 Negative 1 - unit imaginary number
03:53 Imaginary roots of a quadratic equation
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FAQs on Introduction to Complex Numbers Video Lecture - Mathematics (Maths) Class 11 - Commerce

1. What are complex numbers?
Ans. Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit. The real part, a, represents the horizontal axis, while the imaginary part, bi, represents the vertical axis on the complex plane.
2. How are complex numbers represented on a complex plane?
Ans. Complex numbers are represented on a complex plane, also known as an Argand diagram. The real part of a complex number is plotted on the horizontal axis, while the imaginary part is plotted on the vertical axis. The resulting point on the complex plane represents the complex number.
3. What operations can be performed on complex numbers?
Ans. Several operations can be performed on complex numbers, including addition, subtraction, multiplication, and division. Addition and subtraction are done by adding or subtracting the real and imaginary parts separately. Multiplication is performed using the distributive property and the fact that i^2 is equal to -1. Division involves multiplying both the numerator and denominator by the complex conjugate of the denominator to eliminate the imaginary part.
4. How can complex numbers be represented in polar form?
Ans. Complex numbers can be represented in polar form by expressing them as r(cosθ + isinθ), where r is the magnitude or modulus of the complex number and θ is the argument or angle. The magnitude is the distance from the origin to the point representing the complex number on the complex plane, and the argument is the angle between the positive real axis and the line connecting the origin and the point.
5. What is the significance of complex numbers in mathematics and physics?
Ans. Complex numbers have significant applications in various fields of mathematics and physics. They are used in solving equations that have no real solutions, such as quadratic equations with negative discriminants. In physics, complex numbers are crucial for describing phenomena involving oscillations, waves, and electrical circuits. They also play a vital role in Fourier analysis, quantum mechanics, and the study of complex functions in mathematical analysis.
85 videos|243 docs|99 tests

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