Geometric Representation of Complex Expression

Question

Here is the question - Question

I have already worked it out algebraically but was never taught how to answer it geometrically & after watching a few YouTube videos and taking the question literally I came to this answer, is this correct it seems too simple... -

This is my newest attempt after following what Henry has said, my reason for having 3i was because I assumed that 1+i was equivalent to 1+1i so if I added 2 to 1i I'd get 3i? - New attempt

Final edit this seems to be the correct answer -

Answer 1

A couple of comments:

• The circle should pass through $3+i, 1+3i, -1+i, 1-i$ rather than $3,3i,-1,-i$
• I would say explicitly that $|z-(1+i)|$ means the distance between any point on the curve $z$ and the point $1+i$ is $2$, and this implies that the curve is a circle centred at $1+i$ of radius $2$