To find potentially habitable exoplanets, space missions employ the habitable zone (HZ), which is the region around a star (or multiple stars) where standing bodies of water could exist on the surface of a rocky planet. Follow-up atmospheric characterization could yield biosignatures signifying life. Although most iterations of the HZ are agnostic regarding the nature of such life, a recent study argues that a complex life HZ would be considerably smaller than that used in classical definitions. Here, I use an advanced energy balance model to show that such an HZ would be considerably wider than originally predicted given revised CO2 limits and (for the first time) N2 respiration limits for complex life. The width of this complex life HZ (CLHZ) increases by ~35% from ~0.95-1.2 AU to 0.95-1.31 AU in our solar system. Similar extensions are shown for stars with stellar effective temperatures between 2,600-9,000 K. I define this CLHZ using lipid solubility theory, diving data, and results from animal laboratory experiments. I also discuss implications for biosignatures and technosignatures. Finally, I discuss the applicability of the CLHZ and other HZ variants to the search for both simple and complex life.