Quantum mechanics seems to use complex numbers in a fundamentally different way when compared to classical physics. Selected episodes from early stages of the theory are presented to identify different approaches to the use of complex numbers. If for Heisenberg it seemed quite natural to use complex exponentials, Schrödinger clearly struggled with the complex nature of his wave function and tried to assign physical meaning only to its real component. Dirac was probably the first to stress that complex quantities in quantum mechanics cannot be split up into pure real and imaginary parts. Possible educational implications are outlined.