RandomComplex

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RandomComplex[{$z_{min}$, $z_{max}$}]

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[range, n]

gives a list of n pseudorandom complex numbers.

RandomComplex[range, {$n_1$, $n_2$, ...}]

gives a nested list of pseudorandom complex numbers.

RandomChoice
RandomInteger