I'm not sure I understand what you are saying here. I think you are saying that you have three points in thecomplexplane, z1, z3, and i, such that z2= iz1+ 1+ i. Is that correct?

If so, then the distance from z1 to z2 is |z2- z1|= |(i- 1)z1+ 1+i|= , the distance from z1 to i is , and the distance from z2= iz1+ 1+ i to i is . That's all you need to answer this question.

what does "semi-equilateral" mean?then, triangle AMN is :

a)equilateral .

b)semi-equilateral

I have no idea what you mean by this. How do you get a single z fromor

c)right isosceles.

I think the key word is DISTINCT . I know that two points to be distinct z must be different from z(bar) or its conjugate.twopoints? But the word "distinct" certainly is key- if the three points were not distinct, you wouldn't have a triangle!

Any help will be greatly appreciated.

Thank You