If z is a complex variable- the value of -53idzz is

∫_5^3idzz=|l n z|_5^3i =ln 3i ln 5 =ln 3+ln e^iπ/2 in 5 =ln 35+iπ2 I= .511+1.571 i ...

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Cauchy integral Formula and problems

If z is a com...

Question

If $z$ is a complex variable, the value of $\int_{5}^{3 i} \frac{d z}{z}$ is

- 0.511 - 1.57 i

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- 0.511 + 1.57 i

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0.511 - 1.57 i

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0.511 + 1.57 i

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Solution

The correct option is B $- 0.511 + 1.57 i$
$\int_{5}^{3 i} \frac{d z}{z} = | l n z |_{5}^{3 i}$
$= l n 3 i - l n 5$
$= l n 3 + l n e^{i π / 2} - i n 5$
$= l n \frac{3}{5} + i \frac{π}{2}$
$I = - .511 + 1.571 i$

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If z is a complex variable, the value of ∫3i5dzz is

The correct option is B −0.511+1.57i∫3i5dzz=|lnz|3i5 =ln3i−ln5 =ln3+lneiπ/2−in5 =ln35+iπ2 I=−.511+1.571i

If $z$ is a complex variable, the value of $\int_{5}^{3 i} \frac{d z}{z}$ is

The correct option is B $- 0.511 + 1.57 i$
$\int_{5}^{3 i} \frac{d z}{z} = | l n z |_{5}^{3 i}$
$= l n 3 i - l n 5$
$= l n 3 + l n e^{i π / 2} - i n 5$
$= l n \frac{3}{5} + i \frac{π}{2}$
$I = - .511 + 1.571 i$