A complex function f(z) = u (x, y) + i v (x, y) and its complex conjug – McqOptions

MCQOPTIONS

1.	A complex function f(z) = u (x, y) + i v (x, y) and its complex conjugate f*(z) = u(x, y) – i v(x, y) are both analytic in the entire complex plane, where z = x + i y and \({\rm{i}} = \sqrt { - 1}\). The function f is then given by
A.	f(z) = x + i y
B.	f(z) = x2 − y2 + i 2xy
C.	f(z) = constant
D.	(D) f(z) = x2 + y2
Answer» D. (D) f(z) = x2 + y2

Discussion

No Comment Found

Related MCQs

Polar form of the Cauchy-Riemann equations is
If f(z) = (x2 + ay2) + i bxy is a complex analytic function of z = x + iy, where \(i = \sqrt { - 1} \), then
Assuming \(i = \sqrt { - 1} \) and t is a real number, \(\mathop \smallint \limits_0^{\frac{\pi}{3}} {e^{it}}dt\) is:
\(1\;+\;\frac{x^2}{2!}\;+\;\frac{x^4}{4!}\;+\;\frac{x^6}{6!}\;+\;.....\) stands for.
If f(z) is an analytic function whose real part is constant then f(z) is
Let (-1 - j), (3 - j), (3 + j) and (-1 + j) be the vertices of a rectangle C in the complex plane. Assuming that C is traversed in counter-clockwise direction, the value of the countour integral \(\displaystyle\oint_C \dfrac{dz}{z^2 (z-4)}\) is
If then the value of xx is
In the neighbourhood of z = 1, the function f(z) has a power series expansion of the form
An analytic function of a complex variable z = x + iy is expressed as f (z) = u(x,y) + iv (x, y) where i = √-1 . If u = xy, the expression for v should be
If C is a circle of radius r with center z0, in the complex z-plane and if n is a non-zero integer, then \(\mathop \oint \nolimits_C \frac{{dz}}{{{{\left( {z - {z_0}} \right)}^{n + 1}}}}\) equals