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We propose a radix-r digit-recurrence algorithm for complex square-root. The operand is prescaled to allow the selection of square-root digits by rounding of the residual. This leads to a simple hardware implementation of digit selection. Moreover, the use of digit recurrence approach allows correct rounding of the result if needed. The algorithm, compatible with the complex division presented in Ercegovac and Muller (ldquo;Complex Division with Prescaling of the Operands,rdquo; in Proc. Application-Specific Systems, Architectures, and Processors (ASAP'03), The Hague, The Netherlands, June 24–26, 2003), and its design are described. We also give rough estimates of its latency and cost with respect to implementation based on standard floating-point instructions as used in software routines for complex square root.