I have some difficulty in understanding the complex exponential function. So I decide to review the good old exponent function which I learned long ago.
I look up the word
exponent, the online dictionary says this:
- a person or thing that expounds, explains, or interprets: an exponent of modern theory in the arts.
- a person or thing that is a representative, advocate, type, or symbol of something: Lincoln is an exponent of American democracy.
- Mathematics. a symbol or number placed above and after another symbol or number to denote the power to which the latter is to be raised: The exponents of the quantities xn, 2m, y 4 , and 3 5 are, respectively, n, m, 4, and 5.
I am not a native English speaker. To me, these 3 meanings are so distinct. Why are they sharing the same word
exponent? I think the subtle relations among these 3 meanings may help me better understand the human rationale/subconsciousness behind the mathematical concept.
According to here, the exponent part is also called index, or power. I think the latter ones are more acceptable.