# Thread: Complex Number Geometric Representation

1. ## Complex Number Geometric Representation

This is the question -

& this is my attempt at the question am I correct?

2. ## Re: Complex Number Geometric Representation

Originally Posted by Aliionate
This is the question -

& this is my attempt at the question am I correct?
$(z-z_1)=(x+yi)-(1+i)=(x-1)+i(y-1)$
$|z-z_1|^2=(x-1)^2+(y-1)^2=4$

3. ## Re: Complex Number Geometric Representation

Originally Posted by Aliionate
This is the question -

& this is my attempt at the question am I correct?
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.

4. ## 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?

5. ## Re: Complex Number Geometric Representation

Originally Posted by Aliionate
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?

6. ## 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.