- #1

thatboi

- 121

- 18

I have a very simple question regarding the quotient of complex values. Consider the function:

$$f(a) = \sqrt{\frac{a-1i}{a+1i}}$$

where ##i## is the imaginary unit. When I evaluate f(0) in Mathematica, I get ##f(0) = 1i##, as expected. But if I evaluate at a very small value of ##a## such as ##a = 10^{-20}##, I get ##f(10^{-20}) = 10^{-20} - 1i##. I naively thought that ##f## would be continuous in ##a## but it is clear that somehow the imaginary part of ##f## flips sign the moment I introduce some small value for ##a##. How do I explain this behavior? I feel like there is something obvious here I am missing.

Thanks!