- #1

- 477

- 129

## Summary:

- Need help understanding this : "Along the real, or x-axis, partialf/partialy=0"

## Main Question or Discussion Point

On this page https://mathworld.wolfram.com/Cauchy-RiemannEquations.html ...

... above equations

I can see intuitively how (7) reduces to (8) and (9) -- if we're moving along the x axis, we can ignore partial derivative terms that have ##\partial y## in the denominator. (Non-rigorously, we are setting ##\Delta y=0##). But I don't quite understand the two statements quoted above.

... above equations

**8**and**9**it says :These statements seem to be saying that f is independent of y at the x axis, and independent of x at the y axis. Is this necessarily correct for any f?Along the real, or x-axis, ##\partial f / \partial y = 0##

Along the imaginary, or y-axis, ##\partial f / \partial x = 0##

I can see intuitively how (7) reduces to (8) and (9) -- if we're moving along the x axis, we can ignore partial derivative terms that have ##\partial y## in the denominator. (Non-rigorously, we are setting ##\Delta y=0##). But I don't quite understand the two statements quoted above.