SOLUTION: Sketch the set of complex numbers that satisfy |z|<6

Question 1156362: Sketch the set of complex numbers that satisfy |z|<6
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

The region will look like a filled in circle or disk with radius 6. The center is at (0,0).

Points on the edge of the disk represent solutions to |z| = 6, while points inside the disk are solutions to |z| < 6.

Assuming there isnt a line under the less than sign, then you'll have a dashed boundary to indicate points on the boundary do not count. If you want the boundary points to count, then you'll have to write

Diagram:

The blue region is the solution to . The red dashed boundary is not part of .
The equation of the red boundary circle is
The inequality for the blue region is

Note: recall that for any complex number , the magnitude of the complex number is (it might help to plot an example complex number on the xy plane, draw a right triangle, then apply the pythagorean theorem)

Similar problem:
https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1156361.html

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