The sign of complex number plus absolute value is different from that of real number plus absolute value. The absolute value of real number indicates the distance of this number from the origin on the number axis, while the sign of complex number plus absolute value indicates the distance of this complex number from the origin on the complex plane. For example, if the real part of -i is 0 and the imaginary part is-1, then the distance of this complex number from the origin on the complex plane is (0-0) 2+(-65438).

In mathematics

Absolute value or modulus |? x？ | is non-negative, regardless of its sign, that is |x | = x means positive x, | x | = -x means negative x (in this case -x is positive), and | 0 | = 0. For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number can be considered as the distance from zero.

The generalization of absolute value of real number appears in various mathematical settings, such as complex number, quaternion, ordered ring, field and vector space to define absolute value. Absolute value is closely related to concepts such as size, distance and norm in various mathematical and physical environments.