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In analysis what does |x,y| mean/represent?
The vertical bars in this context represent the absolute value of the numbers within them. It is a mathematical notation that indicates the magnitude or distance of a number from 0 on a number line.
The absolute value of a complex number is represented by finding the distance of the number from the origin (0,0) on the complex plane. This is calculated by taking the square root of the sum of the squares of the real and imaginary parts of the complex number.
No, the absolute value of a number cannot be negative as it only represents the distance or magnitude of a number and not its sign. The result of an absolute value calculation is always a positive number.
While both terms refer to the distance or size of a number, they are used in different contexts. Absolute value is used for real numbers and represents their distance from 0, while magnitude is used for complex numbers and represents their distance from the origin on the complex plane.
The absolute value of a vector is represented by finding its length or magnitude. This is calculated using the Pythagorean theorem, which involves taking the square root of the sum of the squares of the vector's components.