Complex Equation: Drawing Set of Points |z+3i|=4

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SUMMARY

The discussion centers on the equation |z + 3i| = 4, which describes a set of points in the complex plane. Here, z represents a complex number of the form x + yi, and the equation signifies all complex numbers that are within 4 units of the point -3i. This relationship indicates that the graph of the equation is a circle centered at -3i with a radius of 4. The participants confirm that the geometric interpretation of the equation is indeed a circle.

PREREQUISITES
  • Understanding of complex numbers, specifically the form x + yi.
  • Familiarity with the concept of absolute value in the context of complex numbers.
  • Knowledge of geometric representations of equations in the complex plane.
  • Basic principles of distance in Euclidean geometry.
NEXT STEPS
  • Study the geometric interpretation of complex numbers in the Argand plane.
  • Learn about the properties of circles in the complex plane.
  • Explore the concept of distance in complex analysis.
  • Investigate transformations of complex numbers and their graphical representations.
USEFUL FOR

Students studying complex analysis, mathematics educators, and anyone interested in visualizing complex equations in the complex plane.

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Homework Statement


Draw the set of points in the complex plane satisfying the equation |z + 3i| = 4


Homework Equations





The Attempt at a Solution

I don't know what z is supposed to be. In class, we've been using z to stand for a complex number (x + yi). Am I supposed to substitute that into the equation? Or, am I supposed to treat z like any real number and find the absolute value?
 
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lockedup said:

Homework Statement


Draw the set of points in the complex plane satisfying the equation |z + 3i| = 4


Homework Equations





The Attempt at a Solution

I don't know what z is supposed to be. In class, we've been using z to stand for a complex number (x + yi). Am I supposed to substitute that into the equation? Or, am I supposed to treat z like any real number and find the absolute value?

Yes, z is a complex number. The equation you give represents all the complex numbers that are within 4 units of -3i. You could also write the equation as |z - (-3i)| = 4 to emphasize that we're talking about distance. The fact that we're talking about the points that are a fixed distance from a fixed point should suggest a particular kind of shape.
 
Thank you, it's coming back to me now. It the graph of a circle. :*)
 

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