Complex numbers: how do I show unique solution?

LHS
Messages
37
Reaction score
0

Homework Statement



[PLAIN]http://img689.imageshack.us/img689/6294/08052011193408.jpg

Homework Equations





The Attempt at a Solution



Hi, I would really appreciate some help on part a, I'm simply getting no where. This is classed as a geometry question, but I haven't covered anything close to this in lectures yet so I'm a little confused, thanks in advance!
 
Last edited by a moderator:
Physics news on Phys.org
Take the conjugate of that equation. Then treat the two equations as linear equations in the two variables z and zbar. Eliminate zbar.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

How do you solve a differential equation with complex numbers?
Replies
3
Views
1K
Complex numbers - I'm sure this is an easy - Argand diagram
Replies
2
Views
2K
Problems with complex numbers and vectors
Replies
11
Views
2K
Complex Number- Express in magnitude/phase form
Replies
1
Views
4K
I Real ODE yields real solution through complex numbers
Replies
3
Views
3K
How to write the complex exponential in terms of sine/cosine?
Replies
7
Views
5K
How Do You Solve and Plot g(z) = 0 for Complex Roots on an Argand Diagram?
Replies
2
Views
2K
Every positive real number has a unique positive n'th root
Replies
8
Views
4K
Example Proof using Complex Numbers
Replies
2
Views
1K
Scaling of a Circle or a Straight Line Using Complex Numbers
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top