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- Author: Titu Andreescu, Dorin Andrica
- Title: Complex Numbers from A to ...Z
- Amazon Link: https://www.amazon.com/dp/0817643265/?tag=pfamazon01-20
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Complex numbers are numbers that contain both a real part and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part with i representing the imaginary unit (the square root of -1).
The main difference between real and complex numbers is that real numbers only have a real part, while complex numbers have both a real and imaginary part. Real numbers are also represented on a one-dimensional number line, while complex numbers are represented on a two-dimensional complex plane.
Complex numbers are important in many fields of science and mathematics, such as engineering, physics, and signal processing. They are also used extensively in solving equations and modeling real-world phenomena, such as electrical circuits and quantum mechanics.
Yes, complex numbers can be added and subtracted. When adding or subtracting complex numbers, we combine the real parts and the imaginary parts separately. For example, (3 + 2i) + (4 + 5i) = (3 + 4) + (2i + 5i) = 7 + 7i.
The conjugate of a complex number is a number that has the same real part but the opposite sign of the imaginary part. The conjugate of the complex number a + bi is a - bi. Conjugates are important in simplifying and dividing complex numbers.