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Homework Help: Simplest way to approximate sqrt of complex numbers

  1. Feb 27, 2010 #1
    I have a ton of homework with square roots of complex numbers. Like sqrt(2 + 3i)

    What is the fastest way to break these down into its approximates like 1.67 + 0.895i without using a TI89/Maple/Matlab/Mathmatica.
  2. jcsd
  3. Feb 27, 2010 #2


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    You could just do a general case for x+iy

    [tex]\sqrt{x+iy} = a+bi \Rightarrow x+iy = (a+bi)^2[/tex]

    and then just equate the real and imaginary parts. Though you will have to solve for 'a' and 'b'. Then you could just either put the numbers into a spreadsheet or calculate by hand when you get 'a' and 'b' in terms of 'x' and 'y'.
  4. Feb 28, 2010 #3


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    Or use the fact that [itex]\sqrt{r(cos(\theta)+ i sin(\theta))}= \sqrt{r}(cos(\theta/2)+ i sin(\theta/2))[/itex].

    For x+ iy, [itex]r= \sqrt{x^2+ y^2}[/itex] and [itex]\theta= arctan(y/x)[/itex]
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