The reciprocal of a real or complex number z!=0 is its multiplicative inverse 1/z = z^(-1), i.e., z to the power -1. The reciprocal of zero is undefined. A plot of the reciprocal of a real number x is plotted above for -2<=x<=2. Two numbers are reciprocals if and only if their product is 1. To put it another way, a number and its reciprocal are inversely related. Therefore, the larger a (positive) number, the smaller its reciprocal. The reciprocal of a complex number z = x + i y is given by 1/(x + i y) = (x - i y)/(x^2 + y^2) = x/(x^2 + y^2) - y/(x^2 + y^2) i. Plots of the reciprocal in the complex plane are given above.

division | division by zero | inversion | inversion pole | polar | power | reciprocal curve | reciprocation