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Math Help - Plotting Complex Variables on Argand Diagrams

  1. #1
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    Plotting Complex Variables on Argand Diagrams

    Hello again guys,

    I have the following problem:

    Problem:

    a) Plot the following complex variables on an Argand diagram

    (i) 2 + j5
    (ii) 3 - j6
    (iii) - 4 + j10
    (iv) - 6 - j3

    b) Convert the (i) and (ii) above into their Polar Equivalents, show ALL working.

    c) Add (i) and (ii) above and express the result in rectangular form.

    d) Subtract (iii) from (ii) above and express the result in rectangular form.

    e) Multiply (i) and (iii) above by first converting to Polar form and express the result in Polar form.

    f) Divide (iii) by (iv) above by first converting to Polar form and express the result in Polar form.

    IT'S PRETTY HARD I KNOW! can anbody help as i'm totally lost.
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  2. #2
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    1)Look at diagram below.

    2)Look at the first line. Let \theta be the angle is forms. Then \tan \theta = \frac{5}{2}=2.5. Thus, \tan^{-1} (2.5)\approx 1.2.
    The radius of this is, \sqrt{2^2+5^2}=\sqrt{29}.
    Therefore, expressed in polar form is,
    \sqrt{29}(\cos 1.2+i\sin 1.2)

    Look at the second line. Let \psi be the angle it forms (acute). Then, \tan \psi =\frac{6}{3}=2. Thus, \psi = \tan^{-1}(2)\approx 1.1. The radius of this is, \sqrt{3^2+6^2}=\sqrt{45}. Therefore, expressed in polar form is,
    \sqrt{45}[\cos (-1.1)+i\sin (-1.1)]
    Note the minus because we need it to give a minus in front of sine because the point is below x-axis.
    Attached Thumbnails Attached Thumbnails Plotting Complex Variables on Argand Diagrams-picture1.gif  
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  3. #3
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    For the polar form of (ii) my answer is:

    6.7 (the distance from 0,0)
    and the angle as 63.43

    Could somebody please verify these answers?

    I perhaps think my angle is wrong, where must the points for the angle start and finish? I'm getting confused as to what happens when minus figures occur.

    THANKS GUYS.
    Last edited by c00ky; August 8th 2006 at 12:00 PM.
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