Question about complex numbers

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SUMMARY

The discussion focuses on the geometric interpretation of complex numbers in the complex plane, specifically addressing the conditions |z|=11, |2z+1|=3, and |i-2z|=5. It is established that |z|=11 represents a circle of radius 11 centered at the origin. The transformation |2z+1|=3 simplifies to |z+1/2|=3/2, indicating a circle of radius 3/2 centered at -1/2 on the real axis. The discussion also implies that |i-2z|=5 represents a circle with a center determined by the complex number i and a radius of 5.

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atwong713
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when indicating the region of the complex plane that corresponds to all points z that satisfy the condition
|z|=11
this region would be the circle of radius 11 around the origin because the |z-w| is the distance between z and w, where z and w are both complex numbers
in general |z-w|=r would be a circle around the pt w on the complex plane with radius r

but how would you indicate a region that satisfies |2z+1| = 3 or |i-2z|=5 for all z?
what do these represent geometrically?
 
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|2z+1|= |2(z+1/2)|= 2|z+ 1/2|= 3 so |z+ 1/2|= 3/2.
 

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