1. ## Complex Numbers

The questions says :

A , M and N are three distinct points of respective affixes i , z1 and z3.

If z2 = iz1 + 1 + i ,

then, triangle AMN is :

a)equilateral .
b)semi-equilateral
or
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.

Any help will be greatly appreciated.
Thank You

The questions says :

A , M and N are three distinct points of respective affixes i , z1 and z3.

If z2 = iz1 + 1 + i ,
I'm not sure I understand what you are saying here. I think you are saying that you have three points in the complex plane, 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|=$\displaystyle \sqrt{2|z1|^2+2}$, the distance from z1 to i is $\displaystyle \sqrt{|z1|^2+ 1}$, and the distance from z2= iz1+ 1+ i to i is $\displaystyle \sqrt{|z1|^2+ 1}$. That's all you need to answer this question.

then, triangle AMN is :

a)equilateral .
b)semi-equilateral
what does "semi-equilateral" mean?

or
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.
I have no idea what you mean by this. How do you get a single z from two points? 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

3. Thank You ~