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

[lockedup]

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?

 

[Mark44]

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.

 

[lockedup]

Thank you, it's coming back to me now. It the graph of a circle. :*)