Solving Complex Variables Homework

In summary, The conversation discusses using Demoivre's theorem and the geometric series formula to show that the sum of all n values of z^(1/n) is zero when n >=2. The attempt at a solution involves trying to make z^(1/n) = p so that p^n = z, and using z = cos(theta) + i sin(theta) for the second part. Further hints are given for solving the second part of the problem.
  • #1
JasonPhysicist
13
0

Homework Statement


I'd like some help with 2 problems:

Show by using Demoivre's theorem and the geometric series formula that the sum of all n values of z^(1/n) is zero when n >=2.
Z is a complex number.

Use the geometric series formula and Demoivre's theorem to show that:

eq3.png

Homework Equations



the geometric series formula:
eq1.png


Demoivre's theorem

eq2.png

The Attempt at a Solution



For the first part,I've tried to make z^(1/n) = p so that p^n = z ,but I had no success showing that the sum equals zero...
For the second part I've made z= cos(theta) + i sin(theta) and I've obtained the left part of the formula,but I can't get the right part...

I'd appreciate any help,because I don't seem to be going anywhere.
Thank you in advance!
 
Last edited:
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  • #2
If [itex]z = cos(\theta)[/itex], what is z2, z3, and so on?
 
  • #3
For the second question, a big hint is to equate equivalent terms.

a + bi = c + di --> a = c, b = d

Don't move things across the equals sign, but work on each side separately
 

1. What are complex variables?

Complex variables are numbers that contain both a real and imaginary component. They are expressed in the form a + bi, where a is the real component and bi is the imaginary component, with b being the imaginary unit.

2. Why are complex variables important?

Complex variables are important in many areas of mathematics, physics, and engineering. They are used to solve problems that involve oscillations, waves, and electrical circuits. They also have applications in signal processing, fluid dynamics, and quantum mechanics.

3. How do you solve complex variables homework?

To solve complex variables homework, you need to have a good understanding of the properties and operations of complex numbers. You should also be familiar with techniques such as adding, subtracting, multiplying, and dividing complex numbers, as well as using the polar form and De Moivre's theorem.

4. What are some common mistakes when solving complex variables?

Some common mistakes when solving complex variables include forgetting to distribute the imaginary unit when multiplying, mixing up the real and imaginary parts, and incorrectly applying the properties of complex numbers. It is important to carefully follow the rules and double-check your work to avoid these mistakes.

5. How can I improve my understanding of complex variables?

To improve your understanding of complex variables, it is helpful to practice solving problems and working through examples. You can also read textbooks or watch online tutorials to learn more about the properties and applications of complex numbers. Seeking help from a tutor or discussing with classmates can also enhance your understanding.

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