1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper

    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


    User Avatar
    Science Advisor

    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]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook