Consider likely applicability of Cauchy's Integral Theorem to evaluate the following integral counter clockwise around the unit circle c.
$$I = \oint\limits_{\text{c}} {\sec {\text{z}}} {\text{dz,}}$$ z being a complex variable. The value of $$I$$ will be
A. $$I$$ = 0 : singularities set = $$\phi $$
B. $$I$$ = 0 : singularities set = $$\left\{ { \pm \frac{{2{\text{n}} + 1}}{2}\pi ;\,{\text{n}} = 0,\,1,\,2\,...} \right\}$$
C. $$I = \frac{\pi }{2}:$$ singularities set = $$\left\{ { \pm {\text{n}}\pi ;\,{\text{n}} = 0,\,1,\,2\,...} \right\}$$
D. None of above
Answer: Option A
This Question Belongs to Engineering Maths >> Complex Variable
A. -x2 + y2 + constant
B. x2 - y2 + constant
C. x2 + y2 + constant
D. -(x2 + y2) + constant
The product of complex numbers (3 - 2i) and (3 + i4) results in
A. 1 + 6i
B. 9 - 8i
C. 9 + 8i
D. 17 + 6i
If a complex number $${\text{z}} = \frac{{\sqrt 3 }}{2} + {\text{i}}\frac{1}{2}$$ then z4 is
A. $$2\sqrt 2 + 2{\text{i}}$$
B. $$\frac{{ - 1}}{2} + \frac{{{\text{i}}{{\sqrt 3 }^2}}}{2}$$
C. $$\frac{{\sqrt 3 }}{2} - {\text{i}}\frac{1}{2}$$
D. $$\frac{{\sqrt 3 }}{2} - {\text{i}}\frac{1}{8}$$
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