Thanks to the use of aspheric optics for lossless apodization, the Phase Induced Amplitude Apodization (PIAA) coronagraph offers full throughput, high contrast and small inner working angle. It is therefore ideally suited for space-based direct imaging of potentially habitable exoplanets. The PIAA concept has recently evolved to a higher performance version, the PIAA complex mask coronagraph (PIAACMC), which uses a combination of phase and amplitude focal plane mask for improved inner working angle and higher contrast. In this paper, PIAACMC design for a telescope with a large central obstruction (of size similar to AFTA's pupil) is described. The potential to image and study potentially habitable planets with a 2.4m telescope is considered. A PIAACMC with a 1.3 λ/D inner working angle appears particularly suitable for the telescope, thanks to a design optimization reducing sensitivity to pointing errors and stellar angular size.