Usage of low-cost hardware in large antenna arrays and low-power wireless devices in Internet of Things (IoT) has led to the degradation of practical beamforming gains due to the underlying hardware impairments, such as in-phase and quadrature-phase imbalance (IQI). To address this timely concern, we present a new nontrivial closed-form expression for the globally optimal least squares estimator (LSE) for the IQI-influenced channel between a multiantenna transmitter and single-antenna IoT device. Thereafter, to maximize the realistic transmit beamforming gains, a novel precoder design is derived that accounts for the underlying IQI for maximizing received power in both single and multiuser settings. Finally, the simulation results, demonstrating a significant -8 dB improvement in the mean squared error of the proposed LSE over existing benchmarks, show that the optimal precoder designing is more critical than accurately estimating IQI-impaired channels. Also, the proposed jointly optimal LSE and beamformer outperforms the existing designs by providing 24% enhancement in mean signal power received under IQI.