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Math Help - Complex Numbers

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by Aladdin View Post
    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|= \sqrt{2|z1|^2+2}, the distance from z1 to i is \sqrt{|z1|^2+ 1}, and the distance from z2= iz1+ 1+ i to i is \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
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  3. #3
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    Thank You ~
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