Complex analysis formula sheet

  • What is the formula for complex numbers?

    Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”.
    The value of i = (√-1).
    For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im)..

  • A function f(z) is said to be analytic in a region R of the complex plane if f(z) has a derivative at each point of R and if f(z) is single valued.
  • Interpretation and reformulation.
    The Cauchy-Riemann equations are one way of looking at the condition for a function to be differentiable in the sense of complex analysis: in other words, they encapsulate the notion of function of a complex variable by means of conventional differential calculus.

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