How to sketch a line from complex numbers

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SUMMARY

The discussion focuses on sketching the line defined by the equation |z - u| = |z|, where u is specified as -1 + j√3. Participants clarify that z represents a general complex number, expressed in the Argand plane as z = x + jy, with x and y being real variables. The task involves solving the equation for y in terms of x or vice versa to visualize the line in the complex plane.

PREREQUISITES
  • Understanding of complex numbers and their representation in the Argand plane.
  • Familiarity with the modulus of complex numbers.
  • Basic algebraic manipulation skills.
  • Knowledge of Cartesian coordinates and graphing techniques.
NEXT STEPS
  • Learn how to manipulate complex number equations geometrically.
  • Study the properties of the Argand plane and its applications.
  • Explore the concept of modulus and its geometric interpretation in complex analysis.
  • Investigate the relationship between complex numbers and linear equations in two dimensions.
USEFUL FOR

Mathematicians, engineering students, and anyone interested in complex analysis or graphical representations of complex numbers.

polaris90
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sketch the line described by the equation |z - u| = |z|
u = -1 + j√3

I don't understand how to do this. I'm not sure of what z is exactly. Can anybody explain to me what it is?
 
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polaris90 said:
sketch the line described by the equation |z - u| = |z|
u = -1 + j√3

I don't understand how to do this. I'm not sure of what z is exactly. Can anybody explain to me what it is?
z is a general complex number. It's often represented if the xy-plane (the Argand plane) by letting x be the real part of z and letting y be the imaginary part of z, i.e. z = x + jy, where x & y are real variables.

So, solve |x + jy -(-1 + j√3)| = |x + jy| for y in terms of x, or x in terms of y.
 

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