# Definition of complex conjugate in English:

## complex conjugate

### noun

Mathematics
• Each of two complex numbers having their real parts identical and their imaginary parts of equal magnitude but opposite sign.

‘replace each element of the matrix by its complex conjugate’
• ‘Only the top half of the plane is shown, since complex eigenvalues always come as complex conjugates, and we have chosen to display the eigenvalue with the positive imaginary part.’
• ‘Of course, points on the real axis don't change because the complex conjugate of a real number is itself.’
• ‘Using a bit more trigonometry, we can determine the angle between two subsequent samples by multiplying one by the complex conjugate of the other and then taking the arc tangent of the product.’
• ‘In a publication in 1932 he gave a lower bound for the regulator of the units of an algebraic number field which depends only on the number of real conjugates and the number of pairs of complex conjugates.’
• ‘The nice property of a complex conjugate pair is that their product is always a non-negative real number.’