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

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Question 1156362: Sketch the set of complex numbers that satisfy |z|<6
Answer by jim_thompson5910(35256) About Me  (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 abs%28z%29+%3C=+6

Diagram:

The blue region is the solution to abs%28z%29+%3C+6. The red dashed boundary is not part of abs%28z%29+%3C+6.
The equation of the red boundary circle is x%5E2%2By%5E2+=+36
The inequality for the blue region is x%5E2%2By%5E2+%3C+36

Note: recall that for any complex number z+=+a%2Bbi, the magnitude of the complex number is abs%28z%29+=+sqrt%28a%5E2%2Bb%5E2%29 (it might help to plot an example complex number on the xy plane, draw a right triangle, then apply the pythagorean theorem)



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