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Math Help - Polar form of -1 + i.

  1. #1
    Newbie Critter314's Avatar
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    Polar form of -1 + i.

    Write z=i-1 in form of {re}^{iv}
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  2. #2
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    It's a math exercise! And it is asking you to change a complex number written in Cartesian form to its "polar form". The simplest way to do that is to graph i- 1 as (-1, 1) (using the x-axis as the real axis, the y-axis as the imaginary axis). Now, your "r" is the distance from (0, 0) to (-1, 1) and your "v" is the angle the line from (0,0) to (-1, 1) makes with the positive real (x) axis. Can you calculate those?
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  3. #3
    Newbie Critter314's Avatar
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    Well r=\sqrt{1^2 + 1^2}=\sqrt{2}
    Angle is 315
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    r is \sqrt{1^2+1^2} = \sqrt{2}

    While \theta = \tan^{-1}\left(\frac{-1}{1}\right), \theta \in (-\pi, \pi)
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  5. #5
    Newbie Critter314's Avatar
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    I should type answer in radians?
    Then z={e\sqrt{2}}^{(i*{-0.758})} ?
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  6. #6
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    I get \displaystyle z= \sqrt{2}e^{\frac{3\pi}{4}i}
    Last edited by pickslides; March 22nd 2011 at 12:46 PM. Reason: bad latex.
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  7. #7
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    Quote Originally Posted by Critter314 View Post
    Write z=i-1 in form of {re}^{iv}
    \text{Arg}(-1+\imath)=\dfrac{3\pi}{4}.

    So \sqrt{2}\exp\left(\dfrac{3\imath\pi}{4}\right).
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  8. #8
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    How do I find an argument?
    315 degrees in radians is \frac{7\pi}{4}
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  9. #9
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    Quote Originally Posted by Critter314 View Post
    How do I find an argument?
    The principle value of the argument of a complex number z=a+bi not on any axis is found by the following.
    Arg(z) = \left\{ {\begin{array}{rl}<br />
   {\arctan \left( {\frac{b}<br />
{a}} \right),} & {a > 0}  \\<br />
   {\arctan \left( {\frac{b}<br />
{a}} \right) + \pi ,} & {a < 0\;\& \,b > 0}  \\  \\<br />
   {\arctan \left( {\frac{b}<br />
{a}} \right) - \pi ,} & {a < 0\;\& \,b < \pi }  \\<br />
 \end{array} } \right.

    Please note that \mathif{i}-1=-1+\mathif{i} and there a=-1~\&~b=1.
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  10. #10
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    Quote Originally Posted by Critter314 View Post
    How do I find an argument?
    315 degrees in radians is \frac{7\pi}{4}
    315= 7(45) which is just 45 degrees short of the full circle. That would correspond to 1- i, not -1+ i.
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