The absolute value (or "modulus" or "magnitude") of a complex number formula_10 is defined as formula_11. Algebraically, if formula_12, then formula_13

The absolute value has three important properties:

for all complex numbers "z" and "w". These imply that formula_19 and formula_20. By defining the distance function formula_21, we turn the set of complex numbers into a metric space and we can therefore talk about limits and continuity. 

The complex conjugate of the complex number formula_12 is defined to be formula_23, written as formula_24 or formula_25. As seen in the figure, formula_24 is the "reflection" of "z" about the real axis, and so both formula_27 and formula_28 are real numbers. Many identities relate complex numbers and their conjugates:

घातांक
लघुगणक
निरपेक्ष मान एवं समिश्र-युग्म
भाग (Division)