Let z = x + iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
A. The residue of $$\frac{{\text{z}}}{{{{\text{z}}^2} - 1}}$$ at z = 1 is $$\frac{1}{2}$$
B. $$\oint_{\text{c}} {{{\text{z}}^2}{\text{dz}} = 0} $$
C. $$\frac{1}{{2\pi {\text{i}}}}\oint_{\text{c}} {\frac{1}{{\text{z}}}\,{\text{dz}} = 1} $$
D. $$\overline {\text{z}} $$ (complex conjugate of z) is analytical function
Answer: Option D
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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