Complex Analysis Answers

U(x,y)+iv(x,y) a. Z^2+2iz b. e^z2 c. In(1+z)

Determine the residue of e^zt/(z-2)^3

Determine the residue of a. 2x+3/z^2-4 b. z-3/z^3+5z^2

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Q. Which of the following is image of straight line x=1 under the transformation f(z)= z^2, where z=x+iy?
a. A circe
b. An ellipse
c. A parabola
d. A hyperbola

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Q. The residue of f(z)=sinh⁡z/z^6 is
a. 1/6!
b. 1/4!
c. 0
d. 1

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Q. Which of the following statement is true for f(z)=sin⁡z/z^4 ?
a. f has essential singularity at z=0.
b. f has pole of order 3 at z=0
c. f has removable singularity at z=0.
d. None of above

Q.Choose the correct answer.
Q. Let C=|z-2|=5, then evaluate the complex integral ∫_C▒〖(z^4 〗+4z)〖cos〗^2 zdz
a. 1
b. 0
c. π
d. -1

Find the polynomial equation over R of lowest degree which is satisfied by 1-i and 3+2i

Find the polynomial equation over R of lowest degree which is satisfied by 1-i and 3+2i

Describe the geometric, polar and exponential representations of:
(\bar -5i+2)⁻¹