For the complex variable function f(z)=u+iv, where u=u(x, y), v=v(x, y) and z=x+iy, then the complex variable function integral ∫f(z)dz =∫(u+iv)(dx+ Idy).

The concept of complex number originated from finding the roots of equations. When finding the roots of quadratic and cubic algebraic equations, the square root of negative numbers appeared. For a long time, people couldn't understand this figure.

Extended data:

Short for complex variable complex-valued function. Let a be a complex set. If any complex number Z in A has one or several complex numbers W corresponding to it according to certain rules, it is said that a complex variable function is defined on complex number set A, and it is recorded as w=? (z).

What does this symbol mean? (z) Is it a Z-pass rule? And a definite complex number. If z = x+iy and w= u+iv, then the complex variable function w=? (z) can be decomposed into w=u(x, y)+iv(x, y).

Baidu Encyclopedia-Complex Variable Function