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Absolute Value of a Complex Number

Absolute Value of a Complex Number
Modulus of a Complex Number

The distance between a complex number and the origin on the complex plane. The absolute value of a + bi is written |a + bi|, and the formula for |a + bi| is \(\sqrt {{a^2} + {b^2}}\). For a complex number in polar form  r(cos θ + isin θ)  the modulus is r.

 

Complex plane showing vector from origin to point a+bi, with |a+bi| as its length and argument as its angle from real axis.

 

 

See also

Real number, imaginary number, argument of a complex number