Complex Analysis Answers

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

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

3) An airplane has 2 engines. P(malfunction) = .0004 for a single engine on a single flight and these malfunctions are independent. A flight will crash if both engines malfunction on that flight. The plane makes 3 roundtrips per day [which is 6 flights]. Find:
[hint: numbers like 4.95E-5 should be written as .0000495]

e) How long can the plane be in service with a probability of any engine malfunction being less than 20%? [hint: find the number of engine uses then find how long]

f) P(first flight crashes) = [write as decimal without scientific notation]

g) P(first flight does not crash) =

h) P(at least one crash in first month) =

i) P(no crash in first 3 months) =

j) How long can the plane be in service with a probability of any crash being less than 2%?
[hint: find the number of flights then find how long]

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.

The base of a right prism is an equilateral triangle whose edges is 10cm each and its lateral edge is 80cm.

_____19. Find its volume in cm3.

a) 2,486.60 b) 3,464.10 c) 4,000.00

_____20. Determine the total area of the prism in cm2.

a) 2,486.60 b) 3,464.10 c) 4,000.00

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