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

Complex Variables and Partial Differential Equations (3140610) MCQs

MCQs of Complex Variable Function and Conformal Mapping

Showing 41 to 50 out of 53 Questions

41.

The value of $|e^{1 + i 2 π}|$ is _____ .

(a)	0
(b)	1
(c)	0.5
(d)	e

42.

A number $\sqrt{2} e^{i π}$ is _____ .

(a)	irrational
(b)	rational
(c)	purely imaginary
(d)	none of these

43.

The principal argument of $\frac{1}{\sqrt{3} + i}$ is _____.

(a)	$\frac{π}{3}$
(b)	$\frac{π}{6}$
(c)	$- \frac{π}{3}$
(d)	$- \frac{π}{6}$

44.

Which of the following is not true (in usual notation)?

(a)	$\arg (z) = - \arg (z)$
(b)	$\arg (z_{1} z_{2}) = \arg (z_{1}) + \arg (z_{2})$
(c)	$Arg (z_{1} z_{2}) = Arg (z_{1}) + Arg (z_{2})$
(d)	$\arg (\frac{z_{1}}{z_{2}}) = \arg (z_{1}) - \arg (z_{2})$

45.

$\arg (z) + \arg (z) =_____(n \in Z) .$

(a)	$\frac{π}{2}$
(b)	$2 nπ$
(c)	$\frac{nπ}{2}$
(d)	None of these

46.

Which of the following is not true?

(a)	$\cos (ix) = i \cosh (x)$
(b)	$\sin (ix) = i \sinh (x)$
(c)	$\tan (ix) = i \tanh (x)$
(d)	$\cosh (ix) = \cos (x)$

47.

One of the value of $\log (1 + i)$ is _____.

(a)	$\log \sqrt{2} + i \frac{π}{4}$
(b)	$\log 2 + i \frac{π}{4}$
(c)	$\log \sqrt{2} - i \frac{π}{4}$
(d)	$\log 2 - i \frac{π}{4}$

48.

The general value of $\log (i)$ is equal to_____ ; $i = \sqrt{- 1}$ .

(a)	$i (\frac{π}{4} + 2 nπ); n \in Z$
(b)	$i (\frac{π}{3} + 2 nπ); n \in Z$
(c)	$i (\frac{π}{2} + 2 nπ); n \in Z$
(d)	None of these

49.

Which of the following is real part of the function $f (z) = 2 iz + 6 z$ ?

(a)	$6 x + 2 y$
(b)	$2 x - 6 y$
(c)	$6 x - 2 y$
(d)	$4 x - 3 y$

50.

Which of the following is imaginary part of the function $f (z) = z^{2} + 2 + i$ ?

(a)	$2 xy + 1$
(b)	$x^{2} - y^{2} + 2$
(c)	$x^{2} + 2 xy$
(d)	None of these

Showing 41 to 50 out of 53 Questions