RandomComplex

RandomComplex[{z_minz_max}]
yields a pseudorandom complex number in the rectangle with complex corners z_min and z_max.
RandomComplex[z_max]
yields a pseudorandom complex number in the rectangle with corners at the origin and at z_max.
RandomComplex[]
yields a pseudorandom complex number with real and imaginary parts from 0 to 1.
RandomComplex[rangen]
gives a list of n pseudorandom complex numbers.
RandomComplex[range, {n1n2, ...}]
gives a nested list of pseudorandom complex numbers.