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Chapter 14: Q30P (page 673)

Using the definition (2.1) of show that the following familiar formulas hold.

Short Answer

Expert verified

By using the definition 2.1, it is showed that the following familiar formula hold.

Step by step solution

01

Definition 2.1 of analytic function

A function is analytic (or regular or holomorphic or monogenic) in a region of the complex plane if it has a (unique) derivative at every point of the region. The statement is analytic at a point means that has a derivative at every point inside some small circle about .

The derivative of is defined (just as it is for a function of a real variable) by the equation,

where and .

02

Apply definition 2.1

Given the function

By the definition 2.1,

Solve the function is as follows:

Here it is clear that the following familiar formula hold by using the definition 2.1.

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