Complex Analysis Answers

Let w=f(z)=z^2+6+6i is a complex function. Then the image of the line x=5

 looks like what?

Given that the complex number z = -2 + 7i is a root to the equation:

z³ + 6 z² + 61 z + 106 = 0

find the real root to the equation.

.Whichofthefolowingistherectangularform ofofthecomplexnumber7.2e

a)0.509+i7.182 b)0.509-2.281c)2.182+i7.217 d)0.217+i7.7.182

A company produces certain types of sophisticated item by three machines. The respective daily production figures are machine A 300 units, Machine B 450 units, and machine C 250 units. Past experience shows that the percentage of defective in the three machines are 0.1,0.2 and 0.7 respectively for machines A B and C. An item is drawn at random from a day's production and is found to be defective. What is the probability that it is not produced by machine C?

 Find the mobius transformation which maps the 

circle |𝑧| < 1 conformally onto |𝑤 − 1| < 1 and 

make the points z=0,1 correspond to w=1/2,0 

respectively. Is the transformation uniquely 

determined

Find the Taylor ‘s theorem expansion of 

logz=(z-1)-

(𝑧−1)

2

2

+

(𝑧−1)

3

2

− ⋯, when|𝑧 − 1| < 1.

Express (6+i )(2-i )/(4+3i )(1-2i) in the form a + ib

Given: 𝑧 = 6 + 7𝑖

Calculate the following:

1) 𝑧^-4

2) 𝑧^1/3, graph the roots.

3) ln 𝑧 , for 𝑛 = 1, 3, 5 & 7

4) 𝑓(𝑧) = 𝑧𝑧̅− 𝑧̅𝑖 + 5𝑖, and check your answer using 𝑧 = 𝑥 + 𝑖y