Complex Analysis Answers

The expression 52 - 4 of (17 - 12) + 4 × 7 is equal to

2*3

Solvetheequationsbelowandhence,showthesolutionsoftheseequationsontheArganddiagram:(i)z4−i=0(ii)z3=−√3−i(iii)z5=−18i(iv)z=16i1+i18(v)z=1+i√3+i16

For two real numbers x and y, f(x+iy) can be written as u(x,y)+iv(x,y) where u and v are functions of real variables.

 What is ((x+1)^2+y^2)u(x,y)?

a) (x+1)^2+y^2

b) x^2+y^2−1

c) y^2−x^2+1

d) (x−y)^2

A fixed point of f(z) is a complex number z such that f(z)=z. How many fixed points does f(z) have?

Let α be a complex number that satisfies both the equations from the previous question. Which of the following are possible arguments of the cube roots of α?

a) π/6

b) 5π/6

c) π/12

d) π/2

e) 5π/12

f) 0

g) π

h) -π/2

Let f(z)=z−1/z+1

. The questions that follow will all revolve around this complex-valued function.

1.

 The value of 25f(2+4i) is equal to a+ib where a,b∈R, and i^2=−1. What is the value of 10a+b?

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