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Complex numbers =]

  1. Jun 2, 2009 #1
    quick note, i am not allowed to use a calculator when doing these questions!

    1: if Z = -i and W = 3+3i
    find arg(z) and arg(w)

    2: 2Z + z[tex]^{-}[/tex](that's the conjugate symbol) = a+2i
    then z =

    3: |z-i| <=1, what would it look like?, describe it's position from the point 0,0

    my attempts

    1:
    z=well i'd use tan^-1 (-1/0) but that's un defined so i'm not quite sure and im not allowed to use a calculator

    w=tan^-1(3/3) = 45 degrees,(tan inverse of 1 is 45 degrees?

    2: no idea hwo to solve this

    3: well because it's -i, i know the centre of the circle is bellow y=0, not sure for the rest
     
  2. jcsd
  3. Jun 2, 2009 #2

    rock.freak667

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    Homework Helper

    Draw z=-i on an argand diagram and the answer should be clear. Your answers should be in radians so convert 45 degrees to radians.


    Put Z=x+iy, then find the conjugate of this. Sub into the equation, equate the real and imaginary terms

    Yes it is a circle. If you aren't sure how to figure it out from the complex form put z=x+iy and form the Cartesian equation

    [tex]|X+iY|=\sqrt{X^2+Y^2}[/tex]
     
  4. Jun 3, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    |a- b| represents the distance from a to b. |z- i| is the distance from the point z to i. |z-i|= 1 represents all points whose distance from i is 1 and so is a circle with center i (NOT -i) and radius 1. Finally |z-i|< 1 is the disk of points inside that circle.
     
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