I think what makes Euler's identity profound to me is that it is a tool for doing so many things. For example, if you want to calculate the log of a negative nu

I think what makes Euler's identity profound to me is that it is a tool for doing so many things. For example, if you want to calculate the log of a negative number: -1 = e^(i * pi) ln(-1) = i * pi ln(-x) = i * pi + ln(x) log_b(-x) = (i * pi + ln(x)) / ln(b) Now you have a formula for calculating the log of a negative number (-x) in any base.