The Fast Fourier Transform Tool is also accessed via the Filter menu in the menu bar. It is the bottom one in the list.
The FFT is done using Fourier / Fourier Transform.
Complex images are saved as are other image types, with File / Save as TIFF, except that the complex images are saved as two TIFF files, <name>-realpart.tif, and <name>-imagpart.tif. I/O / Open, in the I/O button above, will read both parts and display them as a complex image. The image will be (complex double-float), that is in double precision, whether or not it is read from double- or single-precision files. Opening either image with File / Open will open just the real or imaginary part separately.
Depending on the 8-byte float parameter in the File UtilitiesTool ( File / File Utilities ), the real and imaginary parts will be saved as 8-byte floating point numbers (the default), or as 4-byte floating point numbers, if the numbers are within the dynamic range for 4-byte ieee floats, which they generally seem to be.