In this brief, we propose a low-complexity methodology to compute a complex square root using only a circular coordinate rotation digital computer (CORDIC) as opposed to the state-of-the-art techniques that need both circular as well as hyperbolic CORDICs. Subsequently, an architecture has been designed based on the proposed methodology and implemented on the ASIC platform using the UMC 180-nm Technology node with 1.0 V at 5 MHz. Field programmable gate array (FPGA) prototyping using Xilinx' Virtex-6 (XC6v1x240t) has also been carried out. After thorough theoretical analysis and experimental validations, it can be inferred that the proposed methodology reduces 21.15% slice look up tables (on FPGA platform) and saves 20.25% silicon area overhead and decreases 19% power consumption (on ASIC platform) when compared with the state-of-the-art method without compromising the computational speed, throughput, and accuracy. © 2017 IEEE.