Complex Numbers Locus Question

Click For Summary

Homework Help Overview

The problem involves finding the Cartesian equation of a locus defined by the equation |z + 3 + 2i| = Re(z), where z is a complex number. The discussion centers around the interpretation and manipulation of this equation in the context of complex numbers.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss expressing the complex number z in terms of its real and imaginary parts, leading to questions about the meaning of canonical form. There is an exploration of how to manipulate the equation to derive a Cartesian representation.

Discussion Status

Participants are actively engaging with the problem, attempting to derive the Cartesian equation and clarifying the concept of canonical form. Some have provided partial transformations and are seeking further guidance on the next steps.

Contextual Notes

There appears to be some uncertainty regarding the definition of canonical form and how to proceed after reaching a certain equation. Participants are working within the constraints of the homework assignment, which may limit the information they can use.

Amaru58
Messages
4
Reaction score
0

Homework Statement


Find the cartesian equation of the locus |z+3+2i|=Re(z)


Homework Equations





The Attempt at a Solution


You let z= x +iy
therefore Re(z)=x?
 
Physics news on Phys.org
Amaru58 said:

Homework Statement


Find the cartesian equation of the locus |z+3+2i|=Re(z)


Homework Equations





The Attempt at a Solution


You let z= x +iy
therefore Re(z)=x?
Indeed. So you now have

x = \left| x + 3 +iy + 2i\right|

Can you write that in canonical form?
 
OK. I'm not too sure what you mean by canonical form?
Would x = {(x+3)^2 + (y+2)^2}^1/2
Therefore: x^2 = x^2 +6x + 9 +y^2 +4y+4
6x+4y+y^2=-13
I'm not quite sure what to do now
Thanks for the help
 
Amaru58 said:
OK. I'm not too sure what you mean by canonical form?
Would x = {(x+3)^2 + (y+2)^2}^1/2
Therefore: x^2 = x^2 +6x + 9 +y^2 +4y+4
6x+4y+y^2=-13
I'm not quite sure what to do now
Thanks for the help
You're there. The canonical form in Cartesian coordinates is usually f(x,y) = 0 or f(x,y) = const., which is what you have there.
 

Similar threads

Find the complex number which satisfies the given equation
  • · Replies 6 ·
Replies
6
Views
2K
How do we write a sinusoidal solution to a 2nd order DE as a sum of exponentials raised to complex roots?
  • · Replies 2 ·
Replies
2
Views
3K
Show that the given function is continuous
  • · Replies 27 ·
Replies
27
Views
2K
Absolute value of trigonometric functions of a complex number
  • · Replies 9 ·
Replies
9
Views
2K
Show that the real part of a certain complex function is harmonic
  • · Replies 7 ·
Replies
7
Views
3K
Where is ##(z+1)Ln(z)## differentiable?
  • · Replies 5 ·
Replies
5
Views
2K
Complex plane locus question (another one)
  • · Replies 1 ·
Replies
1
Views
2K
Prove the given complex number problem
  • · Replies 3 ·
Replies
3
Views
1K
Find two possible values of ##z## in the complex number problem
  • · Replies 6 ·
Replies
6
Views
2K
Complex numbers: Find the Geometric image
  • · Replies 5 ·
Replies
5
Views
2K