Complex Variables and Partial Differential Equations (3130005) MCQ

MCQs of Complex Function & Conformal Mapping

MCQ No - 1

The principal argument of #$$\frac1{2+3\mathrm i}$$# is _____.

(A)

#$$\tan^{-1}(1.5)$$#

(B)

#$$\tan^{-1}(0.5)$$#

(C)

#$$\tan^{-1}(2.5)$$#

(D)

#$$\tan^{-1}(3.5)$$#


A
MCQ No - 2

The exponential form of #$$\mathrm z=\sqrt3-\mathrm i$$# is _____.

(A)

#$$2\mathrm e^{\left(\frac{\mathrm\pi}3\right)\mathrm i}$$#

(B)

#$$2\mathrm e^{\left(\frac{-\mathrm\pi}3\right)\mathrm i}$$#

(C)

#$$2\mathrm e^{\left(\frac{-\mathrm\pi}6\right)\mathrm i}$$#

(D)

#$$2\mathrm e^{\left(\frac{\mathrm\pi}6\right)\mathrm i}$$#


C
MCQ No - 3

One of the value of #$$\left(-1+\sqrt3\;\mathrm i\right)^\frac13$$# is _____.

(A)

#$$2\mathrm e^{\left(\frac{2\mathrm\pi}3\right)\mathrm i}$$#

(B)

#$$2\mathrm e^{\left(\frac{2\mathrm\pi}9\right)\mathrm i}$$#

(C)

#$$2\mathrm e^{\left(\frac{2\mathrm\pi}7\right)\mathrm i}$$#

(D)

#$$2\mathrm e^{\left(\frac{2\mathrm\pi}5\right)\mathrm i}$$#


B
MCQ No - 4

The principal value of #$$\sin\left(\log\;\mathrm i^{\mathrm i}\right)$$# is _____.

(A)

0

(B)

1

(C)

-1

(D)

none of these


C
MCQ No - 5

The value of #$$\lim_{\mathrm z\rightarrow0}\frac{3\mathrm x^2+4\mathrm y^2}{\left(\mathrm x+\mathrm y\right)^2}$$#

(A)

0

(B)

1

(C)

3

(D)

not exist


D