Complex analysis formula

What is the basic formula of complex analysis?
Any complex number z can be thought of as a point in a plane (x,y), so z = x+iy, where i=√-1.
In a similar fashion, any complex function of a complex variable z can be separated into two functions, as in, f(z)=u(z)+iv(z), or, f(x,y)=u(x,y)+iv(x,y)._{Mar 6, 2022}.
What is the formula for complex functions?
Complex Functions
w = f(z), where z ∈ C and w ∈ Z.
Also, z = x + iy and w = u + iv such that u = u(x, y) and v = v(x, y).
That means u and v are functions of x and y..
The algebra of complex numbers (complex analysis) uses the complex variable z to represent a number of the form a + bi.
The modulus of z is its absolute value.

To create a non-vanishing function, consider exponentiating. 3 Theorems. 1. Cauchy Integral Formula: Let G be region and f : G → C be analytic. If γ1, ,γm.

Mathematical formula in complex analysis

In the mathematical field known as complex analysis, Jensen's formula, introduced by Johan Jensen (1899), relates the average magnitude of an analytic function on a circle with the number of its zeros inside the circle.
It forms an important statement in the study of entire functions.

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Complex analysis formula

What is the basic formula of complex analysis?

What is the formula for complex functions?