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Thread: Complex Number Geometric Representation

  1. #1
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    Complex Number Geometric Representation

    This is the question -
    Complex Number Geometric Representation-capture-.png
    & this is my attempt at the question am I correct?
    Complex Number Geometric Representation-capture-.jpg
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  2. #2
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    Re: Complex Number Geometric Representation

    Quote Originally Posted by Aliionate View Post
    This is the question -
    Click image for larger version. 

Name:	Capture-.PNG 
Views:	9 
Size:	17.8 KB 
ID:	38888
    & this is my attempt at the question am I correct?
    Click image for larger version. 

Name:	Capture--.jpg 
Views:	15 
Size:	416.9 KB 
ID:	38889
    $(z-z_1)=(x+yi)-(1+i)=(x-1)+i(y-1)$
    $|z-z_1|^2=(x-1)^2+(y-1)^2=4$
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  3. #3
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    Re: Complex Number Geometric Representation

    Quote Originally Posted by Aliionate View Post
    This is the question -
    Click image for larger version. 

Name:	Capture-.PNG 
Views:	9 
Size:	17.8 KB 
ID:	38888
    & this is my attempt at the question am I correct?
    Click image for larger version. 

Name:	Capture--.jpg 
Views:	15 
Size:	416.9 KB 
ID:	38889
    It appears that you assumed it was a circle and then drew the circle. But, I am not sure what else the problem would expect you to do to show it "geometrically". Plato showed an algebraic method of demonstration. I personally think his approach is a stronger demonstration, as it does not involve assuming the hypothesis first.
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  4. #4
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    Re: Complex Number Geometric Representation

    I had already worked out the problem algebraically but was curious as to how to answer geometrically as I wasn't taught it & have found only a few videos on answering this type of question. In terms of my answer I think it literally is that but what confuses me is the question itself tells me how to answer the question, so I'm thinking that can't be it?
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  5. #5
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    Re: Complex Number Geometric Representation

    Quote Originally Posted by Aliionate View Post
    In terms of my answer I think it literally is that but what confuses me is the question itself tells me how to answer the question, so I'm thinking that can't be it?
    Can you carefully explain what you mean?
    Or can you tell us what confuses you about what I posted?
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  6. #6
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    Re: Complex Number Geometric Representation

    If you know that |x- y| is the distance between points x and y in the complex plane, then a geometric proof is immediate.
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