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Basics of Complex numbers Video Lecture | Mathematics (Maths) for JEE Main & Advanced
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FAQs on Basics of Complex numbers Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. What are complex numbers? |  |
Ans. Complex numbers are numbers that consist of two parts - a real part and an imaginary part. They are written in the form "a + bi", where "a" represents the real part, "b" represents the imaginary part, and "i" represents the imaginary unit.
| 2. How are complex numbers represented on a coordinate plane? | |
Ans. Complex numbers are often represented on a coordinate plane called the complex plane. The real part of the complex number is plotted on the horizontal axis, and the imaginary part is plotted on the vertical axis. The complex number "a + bi" is then represented as the point (a, b) on the complex plane.
| 3. What is the conjugate of a complex number? | |
Ans. The conjugate of a complex number "a + bi" is obtained by changing the sign of the imaginary part. In other words, the conjugate of "a + bi" is "a - bi". The conjugate of a complex number has the same real part but the opposite sign for the imaginary part.
| 4. How do you add and subtract complex numbers? | |
Ans. To add or subtract complex numbers, simply add or subtract the real parts separately and the imaginary parts separately. For example, to add "a + bi" and "c + di", add the real parts (a + c) and the imaginary parts (b + d) to get the sum. Similarly, for subtraction, subtract the real parts and the imaginary parts.
| 5. How do you multiply complex numbers? | |
Ans. To multiply complex numbers, you can use the distributive property and the fact that "i^2 = -1". Multiply the real parts together, multiply the imaginary parts together, and then combine them. For example, to multiply "a + bi" and "c + di", multiply ac as the real part, bd as the imaginary part, and ad + bc as the cross-product.
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