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Math Help - Square Roots of Negative Numbers & Graphing of Same

  1. #1
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    Question Square Roots of Negative Numbers & Graphing of Same

    1. At present I am working with Imag. and Complex Numbers. I want to determine the square roots of the first 100 negaive numbers. So far have done first 20. Would someone "in the know" please check and make sure I have them done correctly --

    Sq. Rt. Of Equals
    -1 i
    -2 i x sq.rt. of 2
    -3 i x sq.rt. of 3
    -4 2i and -2i
    -5 i x sq.rt. of 5
    -6 i x sq.rt. of 6
    -7 i x sq.rt. of 7
    -8 2i x sq.rt. of 2
    -9 3i and -3i
    -10 i x sq.rt. of 10
    -11 i x sq.rt. of 11
    -12 2i x sq.rt. of 3
    -13 i x sq.rt. of 13
    -14 i x sq.rt. of 14
    -15 i x sq.rt. of 15
    -16 4i or -4i
    -17 i x sq. rt. 17
    -18 3i x sq.rt. of 2
    -19 i x sq.rt. of 19
    -20 2i x sq.rt. of 5

    2. When I am finished with all 100 negative numbers I want to somehow graph them. Can someone give me the method to use? Complex plane? Polar coordinates? Something else?
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  2. #2
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    Quote Originally Posted by DeanSchlarbaum View Post
    1. At present I am working with Imag. and Complex Numbers. I want to determine the square roots of the first 100 negaive numbers. So far have done first 20. Would someone "in the know" please check and make sure I have them done correctly --

    Sq. Rt. Of Equals
    -1 i
    -2 i x sq.rt. of 2
    -3 i x sq.rt. of 3
    -4 2i and -2i
    -5 i x sq.rt. of 5
    -6 i x sq.rt. of 6
    -7 i x sq.rt. of 7
    -8 2i x sq.rt. of 2
    -9 3i and -3i
    -10 i x sq.rt. of 10
    -11 i x sq.rt. of 11
    -12 2i x sq.rt. of 3
    -13 i x sq.rt. of 13
    -14 i x sq.rt. of 14
    -15 i x sq.rt. of 15
    -16 4i or -4i
    -17 i x sq. rt. 17
    -18 3i x sq.rt. of 2
    -19 i x sq.rt. of 19
    -20 2i x sq.rt. of 5

    2. When I am finished with all 100 negative numbers I want to somehow graph them. Can someone give me the method to use? Complex plane? Polar coordinates? Something else?
    In general, if a > 0 and a \in \mathbf{R}

    then \sqrt{-a} = i\sqrt{a}.


    To graph them, you use a compass and straight-edge.

    Draw an Argand Diagram and draw the line \textrm{Re}\,{z} = 1

    Plot the point (1, 1) and join it to the origin. Now you have a 1, 1, \sqrt{2} right angle triangle. If you position your compass with its centre at the origin and tip at (1, 1) and draw the arc to the imaginary axis, you will have plotted i\sqrt{2}.

    Now draw a horizontal line from that point. If you join its intersection with \textrm{Re}\,{z} to the origin, you will have a 1, \sqrt{2}, \sqrt{3} right angle triangle. By drawing the arc to the imaginary axis, you will now have plotted i\sqrt{3}.

    Draw a horizontal line from that point. Join its intersection with \textrm{Re}\,{z} to the origin and you will have a 1, \sqrt{3}, \sqrt{4} right angle triangle. Draw the arc to the imaginary axis and you will have plotted i\sqrt{4} = 2i.

    Follow this process for as long as you like and you will have plotted the square roots of negative integers.
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    "Argand Diagram" ?

    Is this what I would call a "Complex Plane" where vertical axis consists of both positive and negative imaginary numbers and horizontal axis consists of integers? Or, is it something else? If it is something else, where can I find an example of an "Argand Diagram?

    Thanks for your help.
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    Quote Originally Posted by DeanSchlarbaum View Post
    Is this what I would call a "Complex Plane" where vertical axis consists of both positive and negative imaginary numbers and horizontal axis consists of integers? Or, is it something else? If it is something else, where can I find an example of an "Argand Diagram?

    Thanks for your help.
    Yes this is what you would call a Complex Plane.

    A good example of an Argand Diagram can be found on Wikipedia (link below), or just get onto Google or Youtube and do some searches.

    Complex plane - Wikipedia, the free encyclopedia
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