# Complex Number Geometric Representation

• Aug 9th 2018, 02:38 PM
Aliionate
Complex Number Geometric Representation
This is the question -
Attachment 38888
& this is my attempt at the question am I correct?
Attachment 38889
• Aug 9th 2018, 02:59 PM
Plato
Re: Complex Number Geometric Representation
Quote:

Originally Posted by Aliionate
This is the question -
Attachment 38888
& this is my attempt at the question am I correct?
Attachment 38889

\$(z-z_1)=(x+yi)-(1+i)=(x-1)+i(y-1)\$
\$|z-z_1|^2=(x-1)^2+(y-1)^2=4\$
• Aug 9th 2018, 04:04 PM
SlipEternal
Re: Complex Number Geometric Representation
Quote:

Originally Posted by Aliionate
This is the question -
Attachment 38888
& this is my attempt at the question am I correct?
Attachment 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.
• Aug 9th 2018, 04:25 PM
Aliionate
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?
• Aug 9th 2018, 05:53 PM
Plato
Re: Complex Number Geometric Representation
Quote:

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?
• Aug 10th 2018, 04:32 AM
HallsofIvy
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.