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Chapter 14: Q23P (page 687)

Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.

eiz9z2+4atz=2i3

Short Answer

Expert verified

Hence, the residue of the function at z0=2i3 is -0.042785i.

Step by step solution

01

Given information

The given function is: fz=eiz9z2+4.

02

Residue Theorem

If z0 is an isolated singular point of f(z) . Then the integration of the function within any closed curve C is given by:

鈭�cfzdz=b1路2蟺i

Here, b1 is the residue.

03

Find the Residue

As we know, the residue of the function is given by:

Rz=z0=gz0h'z0, for fz=gzhz

According to the question, we have:

gz=eizhz=9z2+4鈬�h'z=18z

Now, the residue atz0=2i3 will be:

R2i3=g2i3h'2i3=ei路2i3182i3=e-2312i=-ie-2312=-0.042785i

Hence, the residue of the function at z0=2i3 is -0.042785i.

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Most popular questions from this chapter

Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.

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