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Math Help - Complex Number: Indicate Graphically

  1. #1
    Newbie ILovePizza's Avatar
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    Complex Number: Indicate Graphically



    I don't understand question c and d. Is c really just asking |x| <= 3? In the back of the book it says the answer for (c) "vertical strip consisting of all (x, y) such that -3<= x <= 3, -∞ <= y <= ∞.
    For (d) I'm completely lost. Can anyone help me with these two?





    NOTE: This is actually from Coddington's ODE's book. I didn't know if I should post this in the Precalculus or Differential Equations section.

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    Re: Complex Number: Indicate Graphically

    Hey ILovePizza.

    You are correct that if z = x + iy then |Re(z)| <= 3 is the same as |x| < 3.

    Hint: For d remember that Im(z) = y if z = x + iy.

    Remember that if you no restrictions on the other variable then you must include all values for that other variable.
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    Re: Complex Number: Indicate Graphically

    I am puzzled as to why you would even consider that. Surely you know that "Re(z)" is not anything like "|z|". If, for example, z= 1+ 10000i, |z|= \sqrt{1000^2+ 1}= \sqrt{1000001}, far larger than "3" while |Re(z)|= 1< 3.

    If z= x+ iy then |Re(z)|= |x|< 3. Where is that on an xy- coordinate system?
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    Re: Complex Number: Indicate Graphically

    I guess what I'm really asking is...

    Why is it that the answer says: vertical strip consisting of all (x, y) such that -3 ≤ x ≤ 3, -∞ ≤ y ≤ ∞? Are the x and y supposed to be (Re z, Im y)? Because for some reason when I enter this in mathematica



    And yet part of the answer is answered for -3 ≤ x ≤ 3. But the other part says -∞ ≤ y ≤ ∞ <---- Where is that coming from? Are those supposed to be Imaginary numbers? And where is the vertical strip? o_o
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    Re: Complex Number: Indicate Graphically

    Quote Originally Posted by ILovePizza View Post
    I guess what I'm really asking is...

    Why is it that the answer says: vertical strip consisting of all (x, y) such that -3 ≤ x ≤ 3, -∞ ≤ y ≤ ∞? Are the x and y supposed to be (Re z, Im y)? Because for some reason when I enter this in mathematica
    And yet part of the answer is answered for -3 ≤ x ≤ 3. But the other part says -∞ ≤ y ≤ ∞ <---- Where is that coming from? Are those supposed to be Imaginary numbers? And where is the vertical strip? o_o
    The program is graphing |x|\le 3. That is not the graph in the complex plane.

    \{z:|\text{Re}(z)|\le 3\}=\{(x+yi):|x|\le 3\} is the set in the complex plane.
    That set can be represented as a set of ordered pairs in the xy\text{-plane}~:\{(x,y):-3\le x\le 3\}.
    That is a vertical strip xy\text{-plane}.
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