Question

A function f(z) is analytic function if

  imaginary part of f(z) is analytic

  real part of f (z) is analytic

  both real and imaginary part of f(z) is analytic

  none of the above

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Answer 1

GIVEN :

A function f(z) is analytic function.

TO FIND :

A function f(z) is analytic function if:

SOLUTION :

Given that a function f(z) is analytic function.

Since given f(z) is analytic if it is differentiable.

⇒ f(z) is continuous.

From the given we have that a function f(z) is analytic function ( if it has complex derivative that is differentiable).

Therefore both the real and imaginary parts are continuous and f is a function of (x, y)

∴ A function f(z) is analytic function if both real and imaginary part of f(z) is analytic

∴ option c) both real and imaginary part of f(z) is analytic is correct.

Answer 2

The third line i.e " both real and imaginary part of f(z) is analytic  " is the correct answer to the given question .

Step-by-step explanation:

• The analytic function is the function that are the converging power series in the locally manner .In the analytic function both real qualitative functions and various analysis functions  are existed.
• The analytic function can only occur when  both the real and the imaginary part of the function f(z) is analytic.
• All the other options are not correct for the analytic function  that's why these are incorrect option .

Learn More :

• brainly.in/question/8696281