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Math Help - Determine the sq root of complex number

  1. #16
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    z = 3 + 4i = 5\,\textrm{cis}\,\arctan{\frac{4}{3}}.
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  2. #17
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    You have already been told that several times. You appear to have extreme difficulty understanding the responses you get.
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  3. #18
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    That because every one iS providing different answers..........mite

    freaking me out
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  4. #19
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    You have been told repeatedly that the magnitude is r= 5 and that the argument (or amplitude), angle, is tan^{-1}(3/4). The polar form is either 5(cos(tan^{-1}(3/4)+ i sin(tan^{-1}(3/4)) or 5 e^{itan^{-1}(3/4)}. Your equation is z^2= 5 e^{i tan^{-1}(3/4)}. z= \sqrt{5}e^{i tan^{-1}(3/4)/2}.

    However, your original question was to find the square roots of 3+ 4i and bigwave, in his first response, showed you how to do that without using the polar form.
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  5. #20
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    The angle is actually

    \theta = \arctan{\frac{\mathbf{Im}z}{\mathbf{Re}z}} = \arctan{\frac{4}{3}}.
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