It is an ABI of 2-b 2+2, and the absolute value under the root sign is = a 2+b 2.

Z=(a+bi) is a complex number, and Z 2 = (a+bi) 2 = A 2+2 ABI+(bi) 2 = A 2+2 ABI-B 2, so in general, Z 2 ≠ A 2+B 2; The absolute value of z is actually the modulus of the complex number z, that is |z|= root sign (a 2+b 2).

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.