| # Magnitude constraints on affine complex vectors Many design problems involve complex variables and magnitude constraints. Such constraints can be often handled via SOCP. The basic idea is that the magnitude of a complex number , with the real and imaginary parts, can be expressed as the Euclidean norm of the -vector : For example, consider a problem involving a magnitude constraint on a complex number , where is a design variable, and the complex-valued function is affine. The values of such a function can be written as where , . For , the magnitude constraint can be written as which is a second-order cone constraint on .