general form of lines and circles in complex plane (1 Viewer)

Mahan1

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Prove the equation of a line and a circle in complex plane has a general form of :



where

Hence, or otherwise, prove

If are complex numbers

which satisfies below condition:



then they are locus of circles in complex plane.
 
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omegadot

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Prove the equation of a line and a circle in complex plane has a general form of :



where

Hence, or otherwise, prove

If are complex numbers

which satisfies below condition:



then they are locus of circles in complex plane.












 

Mahan1

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That proves the above equation is a general form of a circle, but the question says that it also is the form of a line in the complex plane.
To just add on to your proof:

1.prove the equation below represents a line in complex plane:



the equation of the line in general is :



in complex plane, that translates into:



where





multiply by i:



for

we get

 
Last edited:

omegadot

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That proves the above equation is a general form of a circle, but the question says that it also is the form of a line in the complex plane.
To just add on to your proof:

1.prove the equation below represents a line in complex plane:



the equation of the line in general is :



in complex plane, that translates into:



where





multiply by i:



for

we get

 

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