The function fz-z2-1z2-4 is singular at

F(z)=z^2+1z^2+4 For singular points i.e. for poles, z^2+4=0 z=± 2i ...

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Second Derivative Test for Local Maximum

The function ...

Question

The function $f (z) = \frac{z^{2} + 1}{z^{2} + 4}$ is singular at

z = \pm 2

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z = \pm 1

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z = \pm i

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z = \pm 2 i

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Solution

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f (z) = \frac{z - 1}{z^{2} + 1}

C

| z | = 4

f (z) = \frac{z^{2}}{(z^{2} - 3 z + 2)^{2}}

\oint f (z) d z

f (z) = \frac{z^{2}}{z^{2} - 1}

| z - 1 | = 1

f (z) = \frac{7 - z}{1 - z^{2}}

z = 1 + 2 i

|f (z)|

\frac{|z|}{2}

|z|

2 |z|

$If f (z) = \frac{7 - z}{1 - z^{2}}, wehre z = 1 + 2 i, then | f (z) | is$

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