document.write( "Question 1156362: Sketch the set of complex numbers that satisfy |z|<6 \n" ); document.write( "

Algebra.Com's Answer #779059 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "The region will look like a filled in circle or disk with radius 6. The center is at (0,0). \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Points on the edge of the disk represent solutions to |z| = 6, while points inside the disk are solutions to |z| < 6. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "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 $\"abs%28z%29+%3C=+6\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Diagram:
\n" ); document.write( "

\n" ); document.write( "The blue region is the solution to $\"abs%28z%29+%3C+6\"$ . The red dashed boundary is not part of $\"abs%28z%29+%3C+6\"$ .
\n" ); document.write( "The equation of the red boundary circle is $\"x%5E2%2By%5E2+=+36\"$
\n" ); document.write( "The inequality for the blue region is $\"x%5E2%2By%5E2+%3C+36\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "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)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Similar problem:
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1156361.html
\n" ); document.write( " \n" ); document.write( "

\n" );