Thread: Level curve

working through some problems on complex analysis and have no idea what's going on here if someone can give an explanation i may be able to solve,

If f(z) = u(x,y) +iv(x,y), where z = x + iy,

A level curve is a curve of the form u(x,y) = c , c= constant

I don't understand this concept of the level curve any explanation would be greatly appreciated,

Cheers

Here is an example of level curves that i got from a site:



This is a topographical map of some mountain. The contours are the level curves i.e. they are the curves of constant elevation. If f(x,y) = height of mountain at point (x,y), f(x) = c are the level curves of height c.

It is similar for a complex number, except that you are mapping 2 dimensions onto 2 dimension whereas in the above example you are mapping 2 dimensions to 1 dimension. It is somewhat analogous.