# Complex conjugate

In mathematics, the **complex conjugate** of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if and are real, then) the complex conjugate of is equal to The complex conjugate of is often denoted as

In polar form, the conjugate of is This can be shown using Euler's formula.

The product of a complex number and its conjugate is a real number: (or in polar coordinates).

If a root of a univariate polynomial with real coefficients is complex, then its complex conjugate is also a root.