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Math Help - Argument of complex number

  1. #1
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    Argument of complex number

    "Compute Arg(1+2i) x Arg(2+3i)"

    So:

    (1+2i)x(2+3i)

    2+7i-6

    -4+7i

    Tan = 7/-4

    Tan-1= 7 / -4

    I keep getting -60 degrees, but it should be something like 100 degrees. What am I doing wrong?
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  2. #2
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    Quote Originally Posted by coasterguy View Post
    "Compute Arg(1+2i) x Arg(2+3i)"

    Mr F asks: Is this meant to be a product of arguments? Or are you trying to find the arument of (1 + 2i)(2 + 3i)? Your 'solution' suggests the latter.

    So:

    (1+2i)x(2+3i)

    2+7i-6

    -4+7i

    Tan = 7/-4

    Tan-1= 7 / -4

    I keep getting -60 degrees, but it should be something like 100 degrees. What am I doing wrong?
    -4 + 7i lies in the second quadrant. So you want the angle \alpha lying in the second quadrant such that \tan \alpha = - \frac{7}{4}. It is not a 'special angle' so you will have to use your calculator and get a decimal approximation.

    But this is not the answer to the question as posted. The answer to the question you've posted is \tan^{-1} (2) \cdot \tan^{-1} \left( \frac{3}{2} \right).
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