The absolute value of a complex number is the magnitude of the number, which is found from sqrt(a² + b²) for the complex number a + bi
The absolute value of zero is zero. The absolute value of any other real number - or even of any other complex number - is different from zero.
That is because of the way the absolute value is defined. The absolute value of a positive number is positive, the absolute value of a negative number is also positive. The absolute value of zero is zero. Even in the complex numbers, the absolute value is defined in such a way that it is a real and positive number.
Because a complex number is a two dimensional entity. The concept of less than or greater than, for ordinary numbers, is one-dimensional. It can be applied to the magnitude (absolute value) of a complex number.
The absolute value of the sum of two complex numbers is less than or equal to the sum of their absolute values.
The absolute value of a complex number ( a + bi ) is calculated using the formula ( \sqrt{a^2 + b^2} ). For the complex number ( 3 - 4i ), ( a = 3 ) and ( b = -4 ). Therefore, the absolute value is ( \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 ). Thus, the absolute value of ( 3 - 4i ) is 5.
The absolute value of a complex number a+bi is the square root of (a2+b2). For example, the absolute value of 4+9i is the square root of (42 + 92) which is the square root of 97 which is about 9.8489 (The absolute value of a complex number is not complex.)
The absolute value of zero is zero. The absolute value of any other real number - or even of any other complex number - is different from zero.
The absolute value of zero is zero. The absolute value of any other real number - or even of any other complex number - is different from zero.
That is because of the way the absolute value is defined. The absolute value of a positive number is positive, the absolute value of a negative number is also positive. The absolute value of zero is zero. Even in the complex numbers, the absolute value is defined in such a way that it is a real and positive number.
Because a complex number is a two dimensional entity. The concept of less than or greater than, for ordinary numbers, is one-dimensional. It can be applied to the magnitude (absolute value) of a complex number.
The absolute value of the sum of two complex numbers is less than or equal to the sum of their absolute values.
The absolute value of a complex number ( a + bi ) is calculated using the formula ( \sqrt{a^2 + b^2} ). For the complex number ( 3 - 4i ), ( a = 3 ) and ( b = -4 ). Therefore, the absolute value is ( \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 ). Thus, the absolute value of ( 3 - 4i ) is 5.
Order has to do with the relation of one number to another. Statements like a>b is an ordered statement. Absolute value is the distance that a number is from 0. So the absolute value of 3 is 3, and the absolute value of -3 is 3.
Given that absolute values are always positive, and that there is no equivalence between complex numbers and real numbers, I would have to say no, there isn't. The absolute value of a real number is its distance from zero on a number line. Since a distance is always positive, we say the absolute value is always positive. Graphically, a real number is just a point on a number line. The absolute value of a complex number is its distance form the origin in a coordinate plane, where coordinate axes are the x-axis with real numbers, and the y-axis with imaginary numbers. In this diagram, called Argand diagram, a complex number a + bi (where a and b are real numbers) is the point (a, b) or the vector from the origin to the point (a, b). Using the distance formula, the absolute value or the distance of a complex number a + bi is equal to the principal square root of (a2 + b2).
You can get the absolute value of a complex number by using Pythagoras's Theorem, which in this case is: absolute value (i.e., distance from zero) = the square root of (real part squared + imaginary part squared).
no number; absolute value is always positive. The absolute value of a negative number is positive. For example absolute value of -4 is +4
The absolute value of a number is the positive (or non-negative) value of the number. The absolute value of 0 or a positive number is the number itself. The absolute value of a negative number is its positive equivalent.