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 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.       See also Real number, imaginary number, argument of a complex number