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Basics of Complex Numbers Video Lecture | Algebra - Mathematics

FAQs on Basics of Complex Numbers Video Lecture - Algebra - Mathematics

1. What are complex numbers?

Ans. Complex numbers are numbers that consist of a real part and an imaginary part. They are expressed in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit.

2. How do you add complex numbers?

Ans. To add complex numbers, you simply add the real parts together and the imaginary parts together. For example, (3 + 2i) + (1 - 4i) would be (3 + 1) + (2i - 4i) = 4 - 2i.

3. Can complex numbers be multiplied?

Ans. Yes, complex numbers can be multiplied. To multiply complex numbers, you use the distributive property and the fact that i^2 equals -1. For example, (2 + 3i) * (4 - 5i) would be (2 * 4) + (2 * -5i) + (3i * 4) + (3i * -5i) = 8 - 10i + 12i - 15i^2 = 8 + 2i - 15(-1) = 23 + 2i.

4. How do you find the conjugate of a complex number?

Ans. To find the conjugate of a complex number, you change the sign of the imaginary part. For example, the conjugate of 3 + 4i would be 3 - 4i.

5. What is the modulus or absolute value of a complex number?

Ans. The modulus or absolute value of a complex number is the distance between the origin and the point representing the complex number in the complex plane. It is calculated by taking the square root of the sum of the squares of the real and imaginary parts. For example, the modulus of 2 + 3i would be sqrt(2^2 + 3^2) = sqrt(4 + 9) = sqrt(13).

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Sep 30, 2025 Last updated

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