In mathematics, the imaginary part of a complex number z, is the second element of the ordered pair of real numbers representing z, i.e. if z = (x,y), or equivalently, z = x + iy, then the imaginary part of z is y. It is denoted by Imz or . The complex function which maps z to the imaginary part of z is not holomorphic.

In terms of the complex conjugate , the imaginary part of z is equal to .

For a complex number in polar form, z = (r,θ), or equivalently, z = r(cosθ + isinθ), it follows from Euler's formula that z = re^iθ, and hence that the imaginary part of re^iθ is rsinθ.

See also

• Real part
• Imaginary number
• Complex number