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Complex numbers | 19/27 | UPV
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Título: Complex numbers
Descripción automática: In this video, the instructor introduces the concept of complex numbers and their basic operations, particularly addition and subtraction. The presentation begins by setting the educational objectives, namely defining complex numbers and understanding their sum. The prerequisites mentioned are a basic understanding of real numbers and their operations as learned in high school.
The instructor defines a complex number in binomial form as a combination of two real numbers, "a" and "b," where "b" is multiplied by "i," the imaginary unit that satisfies the equation "i"² = -1. Complex numbers are usually represented by "z," and the set of all complex numbers by the capital letter "C." The real part of a complex number is "a," and "b" is the imaginary part, associated with the imaginary unit "i." Several examples of complex numbers are presented, demonstrating how the real and imaginary parts can vary, including pure imaginary numbers and real numbers as special cases within the complex number system.
It is explained that complex numbers have properties similar to real numbers, such as equality—where complex numbers are equal only when their respective real and imaginary parts match—the commutative and associative properties of addition, and the existence of a neutral element (zero). The concept of the additive inverse (opposite number) for complex numbers is introduced, which involves changing the signs of both the real and imaginary parts.
The instructor outlines the procedures for addition and subtraction of complex numbers, which involve adding or subtracting their corresponding real parts and imaginary parts. Concrete examples are provided to illustrate the process, demonstrating the sum and difference of two complex numbers with the resulting real and imaginary components.
The video concludes with a summary emphasizing the importance of understanding the definition of complex numbers, the operation of their addition and subtraction, and their properties, which largely parallel those of real numbers.
Autor/a: Moll López Santiago Emmanuel
#Complex Numbers #Addition of Complex Numbers #APPLIED MATHEMATICS
Descripción automática: In this video, the instructor introduces the concept of complex numbers and their basic operations, particularly addition and subtraction. The presentation begins by setting the educational objectives, namely defining complex numbers and understanding their sum. The prerequisites mentioned are a basic understanding of real numbers and their operations as learned in high school.
The instructor defines a complex number in binomial form as a combination of two real numbers, "a" and "b," where "b" is multiplied by "i," the imaginary unit that satisfies the equation "i"² = -1. Complex numbers are usually represented by "z," and the set of all complex numbers by the capital letter "C." The real part of a complex number is "a," and "b" is the imaginary part, associated with the imaginary unit "i." Several examples of complex numbers are presented, demonstrating how the real and imaginary parts can vary, including pure imaginary numbers and real numbers as special cases within the complex number system.
It is explained that complex numbers have properties similar to real numbers, such as equality—where complex numbers are equal only when their respective real and imaginary parts match—the commutative and associative properties of addition, and the existence of a neutral element (zero). The concept of the additive inverse (opposite number) for complex numbers is introduced, which involves changing the signs of both the real and imaginary parts.
The instructor outlines the procedures for addition and subtraction of complex numbers, which involve adding or subtracting their corresponding real parts and imaginary parts. Concrete examples are provided to illustrate the process, demonstrating the sum and difference of two complex numbers with the resulting real and imaginary components.
The video concludes with a summary emphasizing the importance of understanding the definition of complex numbers, the operation of their addition and subtraction, and their properties, which largely parallel those of real numbers.
Autor/a: Moll López Santiago Emmanuel
#Complex Numbers #Addition of Complex Numbers #APPLIED MATHEMATICS
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