modulus of a complex number

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If z is a complex number and z=x+yi, the modulus of z, denoted by |z| (read as ‘mod z’), is equal to (As always, the sign √means the non-negative square root.) If z is represented by the point P in the complex plane, the modulus of z equals the distance |OP|. Thus |z|=r, where (r, θ) are the polar coordinates of P. If z is real, the modulus of z equals the absolute value of the real number, so the two uses of the same notation | | are consistent, and the term ‘modulus’ may be used for ‘absolute value’.

Subjects: Mathematics.

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