Complex signals are ubiquitous in various fields of engineering and science. The complex Kalman filters are used to process complex signals. The complex Kalman filter is associated with linear models in linear estimation, while the complex extended Kalman filter is associated with augmented models or widely linear models in nonlinear estimation. Both complex Kalman filter and complex extended Kalman filter utilize the Kalman filter gain in order to compute the estimation and the prediction of the n-dimensional state using the m-dimensional measurement. In this work, variations of complex Kalman filter and of complex extended Kalman filter are derived; the proposed algorithms eliminate the Kalman filter gain. The proposed Kalman filter with gain elimination may be faster than the traditional Kalman filter; in fact the model dimensions determine the fastest filter. Also, steady-state complex Kalman filters are derived, which require the solution of the complex Riccati equation. Per step and doubling iterative algorithms for the solution of the complex Riccati equation are presented.