MCQs of Complex Variable Function and Conformal Mapping (Complex Variables and Partial Differential Equations - 3140610)

Complex Variables and Partial Differential Equations (3140610) MCQs

MCQs of Complex Variable Function and Conformal Mapping

Showing 21 to 30 out of 53 Questions

21.

Which of the following is related to Cauchy-Riemann equations?

(a)	$u_{x} = u_{y}, v_{x} = v_{y}$
(b)	$u_{x} = v_{y}, u_{y} = - v_{x}$
(c)	$u_{x} = v_{y}, u_{y} = v_{x}$
(d)	none of these

22.

If z is non zero complex number such that $Re (z) = 0$ , then _____ .

(a)	$Re (z^{2}) = 0$
(b)	$Re (z^{2}) = Im (z^{2})$
(c)	$Im (z^{2}) = 0$
(d)	none of these

23.

If z is non-zero complex number such that $Arg (z) = \frac{π}{4}$ , then _____ .

(a)	$Re (z^{2}) = 0$
(b)	$Re (z^{2}) = Im (z^{2})$
(c)	$Im (z^{2}) = 0$
(d)	none of these

24.

Let $z = x + i y$ be a complex number and $\bar{z} = z$ , then _____ .

(a)	z is completely real
(b)	z is purely imaginary
(c)	$z = 0$
(d)	none of these

25.

Let $z = |\begin{matrix} 1 & 1 - i \\ 1 + i & - 2 \end{matrix}|$ , then ______ .

(a)	z is purely imaginary
(b)	z is purely real
(c)	z=0
(d)	none of these

26.

Let $z = x + i y$ be a complex number. If $|z + 4| \leq 3$ , then the maximum value of $|z + 1|$ is _____ .

(a)	0
(b)	4
(c)	6
(d)	10

27.

If $|w| = 2$ , then the set of points $z = w - \frac{1}{w}$ lie on _____ .

(a)	circle
(b)	parabola
(c)	hyperbola
(d)	ellipse

28.

The value of $\sum_{n = 1}^{3} [i^{n} + i^{n + 1}]$ , where $i = \sqrt{- 1}$ , equals to _____ .

(a)	$- 1 - i$
(b)	$1 + i$
(c)	$1 - i$
(d)	0

29.

The smallest positive integer n for which ${(\frac{1 + i}{1 - i})}^{n} = 1$ is _____ .

(a)	2
(b)	4
(c)	6
(d)	8

30.

If $|z_{1}| = 1, |z_{2}| = 1, z_{1} + \bar{z_{2}}$ is non-zero and $z = \frac{z_{1} \bar{z_{2}} + 1}{z_{1} + \bar{z_{2}}}$ , then conjugate of z equals to _____ .

(a)	z
(b)	2z
(c)	3z
(d)	4z

Showing 21 to 30 out of 53 Questions