All the poles and zeros of a function are in the left half plane or on its boundary the imaginary axis.

Zero of a function, a root of a function.

Newton's method is a method for finding a zero of a function f(x).

Zeroes of a function are used because they are another way to talk about solving an equation, which is a main goal in algebra.

A zero of a function f is a point x in the domain of the function such that .

Argand diagrams are frequently used to plot the positions of the poles and zeroes of a function in the complex plane.

One derivation shows it is a special case of Newton's method (also called the Newton-Raphson method) for finding zeros of a function beginning with an initial guess.

It refers also to the zero of a function describing the trajectory of a rocket, suggesting a continuation of that trajectory beyond the point of impact and destruction.

Besides its applications in analytic number theory, it has been used in function theory, numerical analysis, differential equations, transcendence theory, and estimating the number of zeroes of a function in a disk.

In the nineteenth century, the great German mathematician Bernhard Riemann conjectured, but did not prove, that all the zeroes of a function known as the zeta function lay in a certain region of the complex plane.