## Quick Reference

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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