Complex Analysis Answers

Find the equation of the circle that contains the points (4, 6), (-2, 4), (8, -6)

Find the equation of a circle with centers (1, 1) and contains points (2, 3)

Find all the 5th roots of (5-i).

The following cases represents the two velocity components, determine ghe third components of velocity such that they satisfy the continuity equation :
(i) u = 4x^2 , v = 4xyz
(ii) u = 4x^2 + 3xy , w = z^3 - 4xy - 2yz.

Sketch the stream lines represented by ψ = xy. Also find out the velocity and its direction at point (2, 3).

A fluid flow is given by : V = 10x^3 i - 8x^3 yj. Find the shear strain rate and state whether the flow is rotational or irrotationsl.

For the velocity components given as : u = ay sin xy, v = ax sin xy. Obtain an expression for the velocity potential function.

Q: Evaluate the following integral using residue theorem
∫ Z^2 e^z dz ; C : |z| = 1 ,Answer(πi/3)

Q: Evaluate the following integral using residue theorem
∫ coth z / (z-i) dz ; C : |z| = 2