An imaginary number is a part of a complex number. Complex numbers are an extension of the real numbers. A complex number has a real and an imaginary part. The imaginary unit (i) is equal to the square root of -1. The complex conjugate is a pair of complex numbers with identical real parts and imaginary parts which differ only in sign (e.g.: 3 + 7i and 3 - 7i).

The symmetry in k-space is a fundamental property of Fourier transformations. For a two-dimensional example, let g(x,y) be a complex function, i.e. the value of g at any (x,y) is a complex number. If nothing is known about the function g, data throughout all of k-space is needed to fully characterize it.
If the function g is 'real', meaning that at every (x,y) the imaginary component of g(x,y) is zero, then you only need half as much data to characterize g. The result is redundancy between the data on one half of k-space and the other. Specifically, if G(kx,ky) is the Fourier transformation of g(x,y), and g(x,y) is real, then G(kx,ky)=G*(- kx,- ky), where * indicates a complex conjugate. The data in mirrored positions in k-space, i.e. (kx,ky) versus (- kx,- ky), are conjugates of each other.

See Imaginary Numbers and Complex Conjugate.

The complex numbers extend the real numbers by including the imaginary unit i (satisfying i2 = - 1). The term 'complex' when used as an adjective means that the field of complex numbers is as the underlying number field considered. In MRI, complex data are used for example in the Fourier transforms.