The mathematical duality of human emotion: pure joy when seeing the logarithm of 4 equals 2 (a perfectly reasonable result), followed by existential dread when confronting log(-1) and imaginary numbers.
Nothing captures the mathematician's journey quite like the transition from comfortable territory (real logarithms) to the bizarre realm where we need complex analysis. The introduction of j = ln(-1) is where mathematicians either have their spiritual awakening or their first nervous breakdown. Usually both, simultaneously.