Obtaining an intuition for what it means to use an imaginary exponent takes work. Exponents give us expoential decay/growth in the real number line, but period

Obtaining an intuition for what it means to use an imaginary exponent takes work. Exponents give us expoential decay/growth in the real number line, but periodicity in the imaginary domain, which is strange. In physics, this lets us analyze decaying or amplifying oscillations in a unified way. (Laplace transform and all that.)