Complex Variable Function and Integral Transformation Exam 2020-2021

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Questions and Answers

What is the value of z + z + z when z = $\frac{i}{1 + i}$?

  • $1 - i$
  • $\frac{3}{1 - i}$ (correct)
  • $-1$
  • $\frac{1 - i}{2}$

For the function $f(z) = \frac{1}{2z - 3}$, what is the number of singular points in $z - i = 2$?

  • 3
  • 1
  • 2 (correct)
  • 4

If f(z) is analytic in domain B and not zero, and C is any simply closed curve in B, what is the value of $\oint_C f(z) dz$?

  • Not sure
  • $3\pi i$
  • 0
  • $2\pi i$ (correct)

What is the value of z + z + z when z = $\frac{i}{1 + i}$?

<p>$\frac{1 - i}{2}$ (C)</p> Signup and view all the answers

For the function $f(z) = \frac{1}{2z - 3}$, what is the number of singular points in $z - i = 2$?

<p>2 (A)</p> Signup and view all the answers

If $f(z)$ is analytic in domain $B$ and not zero, and $C$ is any simply closed curve in $B$, what is the value of $\oint_C f(z) dz$?

<p>$2\pi i$ (A)</p> Signup and view all the answers

When $z = \frac{i}{1 + i}$, what is the value of $z + z + z$?

<p>$\frac{1 - i}{2}$ (C)</p> Signup and view all the answers

If a function $g(z)$ is given by $g(z) = -2\pi i \cot(\pi z)$, what is the number of singular points in $z - i = 2$?

<p>3 (A)</p> Signup and view all the answers

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