# complex

1. ### Hard probability problem

In the probability game, a player must spin a spinner with numbers 1-10 on it (equal chances). Based on the result of the first spinner, they have to guess if the next spinner number is going to be higher or lower. If they guess correctly they get 1 ticket. What is the probability of the player...
2. ### Logarithmic Function

Show that logarithmic function is analytical. What are branch cut and principle branch of natural logarithm of z (ln z)?
3. ### Complex Variables :)

Q) Why complex analysis is concerned with complex functions that are differentiable?
4. ### Complex analysis- residue theorem

Is it possible to solve the above using residue theorem? if yes then how to start?
5. ### LCD is Complex Fractions

Just started an intermediate algebra class and I'm already lost. I have complex fractions to simplify, I can do it until I get to the ones requiring the use of LCD. I cannot for the life of me figure out how the LCD is found. I have a sample problem of...
6. ### Complex linear integration

Hi everyone i need some help on some complex integration. I am struggling on how to go about these two questions as its a non-simple integral and we haven't covered this properly in Uni yet. On Question 3 i think I just have to present two options on whether z = w is included in C or not but...
7. ### Cauchy's Theorem in complex functions

Hi everyone, I'm starting off with complex numbers and functions and would need a little help from you guys. I have the following equation: Evaluate the closed integral of: e^z/(z*(z^2+4)) where C = {abs(z)=1} clockwise and then C={abs(z)=3} anticlockwise. I was told to first check...
8. ### inequality about complex numbers

Hi, given complex numbers z1,...zn'shob that there exists a subset J of {1,...,n} such that : attached attempt :i tried to use the residue theorem for the function (z-z1)*.....*(z-zn)/z^n on a circle of around the origin
9. ### complex series

Hi, I need to find the region where the following complex series converges: I computed the absolute value of the function and used the nth root test/Is it correct? if not,how can i find the region? Thank's in advance
10. ### Complex polynomial

Firstly, I want to say that I am from Spain, so I will do my best to express myself correctly. If p(z) is a real fifth degree polynomial with an only real root. If p(0)≠0, the quantity of real solutions of p(z-iz)=0 (where z is the conjugate) is: a) at least 1 b) at the most 2 c) it can be 4...
11. ### Equation with complex numbers

Any thoughts, clues on this one? Find all complex numbers such that Thanks!!!!!
12. ### Complex number

Some thoughts or clues on this so I can guide my son and ask him the right questions so he can solve this:What complex number equals ? Thanks!!!
13. ### Complex Analysis Singularities

I've found that the singularities for the complex function $\frac{1}{cos(1-\frac{1}{z})}$ are $z=0$ and $z=\frac{2}{2-(2k+1)\pi}$ where $k\in\mathbb{C}$ but how do you know what kind of singularity they are? (i.e. poles, removable singularities or essential singularities) Any help would be much...
14. ### solving complex equations

does anyone know to solve an equation of 1/ surd(x) = -2log( [(1.33x10^-3)/3.7 ] + [2.51 / (7.4x10^6)(surd x ) ] ) this is an physics equation , but i dont know how to solve it mathematically how to find the value of x ?
15. ### Complex Number puzzle

Hello everyone, ive got a new Maths sequence number puzzle which is kind of tough to crack, can you validate and crack for the next sequence number? List 1 - 26 40 38 17 3 4 10 List 2 - 43 39 13 6 18 2 8 List 3 - 33 10 18 40 17 8 2 Based this, can you understand the logic and Make list 4?? Good...
16. ### Complex Number Puzzle

Hello everyone, ive got a new Maths sequence number puzzle which is kind of tough to crack, can you validate and crack for the next sequence number? List 1 - 26 40 38 17 3 4 10 List 2 - 43 39 13 6 18 2 8 List 3 - 33 10 18 40 17 8 2 Based this, can you understand the logic and Make list...
17. ### Complex Numbers puzzle

Hello everyone, ive got a new Maths sequence number puzzle which is kind of tough to crack, can you validate and crack for the next sequence number? List 1 - 26 40 38 17 3 4 10 List 2 - 43 39 13 6 18 2 8 List 3 - 33 10 18 40 17 8 2 Based this, can you understand the logic and Make list 4...
18. ### Proving a complex inequality

$$|e^z -1| \leq e^{|z|} -1 \leq |z|e^{|z|}$$ for all $z \in C$. I tried substituting $e^z = e^x (\cos y + i \sin y)$ and $|z| = \sqrt {x^2 + y^2}$ but after 2 pages of manipulations, I got back where I started, only messier forms. Any hints are appreciated.
19. ### Complex Roots of a Quadratic

Hi I am trying to solve a 2nd order ODE and after multiplying through by e^(theta x) the co-efficients I am left with are: a=1, b=4, c=25 I can then solve this as far as -4 plus or minus sqrt(16-100)/2 Leaving -4+- sqrt(-84)/2 I can see this can be simplified to say -4+2i(sqrt21)/2 = -2+i...
20. ### Plotting in Complex Plane

Hi, Can anyone give me some tips about plotting a quadratic and a fourth root in the complex plane. The quadratic is: z^2+2iz+1=0 The other: z^4=16 Thanks Beetle