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Given that (z_1=r_1(cos∅_1+isin∅_1 and (z_2=r_2(cos∅_2+isin∅_2) evaluate (z_1z_2)

Find the fifth root of -1

Find the polar form of complex number (2+2isqrt(3))

Evaluate the integration of (2z+3)dz from 1-2i to 3+i. a. along the path x=2t+1, y=4t^2-t-2, 0<=t<=1. b.along the strightline joining 1-2i and 3+i

Use contour integration a. evaluate integration of x^2dx/x^4+1 from 0 to infinity. b. Show that the integration of cosn/1-2 cos+a^2 from 0 to 2π

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

Choose the correct answer.
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

Choose the correct answer.
Q. The residue of f(z)=sinhz/z^6 is
a. 1/6!
b. 1/4!
c. 0
d. 1