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For a complex variable z = x + iy, which of the following statements is true?

For a complex variable z = x + iy, which of the following statements is true? Correct Answer Both sin h <s>Z</s> and cos h <s>Z</s> are entire functions

Explanation:

Analytic Function

If a complex function f(Z) is differentiable at point Z0 and also differentiable at every point in some neighbourhood of a point Z0 then the function f(Z) is called an analytic function at point Z = Z0

Entire Function

If a function f(Z) is analytic at every point in the whole finite complex plane then the function f(Z) is called an entire function. As sin h Z and cos h Z are analytic everywhere in the complex plane so they are called entire functions.

Additional Information

 Analytic Function

  • A function f(z) which is single-valued and possesses a unique derivative with respect to z at all points of the region R, is called the analytic function of z in that function.
  • An analytic function is also called a regular function or a holomorphic function.
  • A function that is analytic everywhere in the complex plane is known as an entire function.
  • As a derivative of a polynomial exists at every point, a polynomial of any degree is an entire function.
  • A point at which an analytic function ceases to possess a derivative is called a singular point of the function.

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