murshid_islam
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what does \sqrt{i^2} equal to? is \sqrt{i^2} = i or \sqrt{i^2} = \pm i?
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you said, \sqrt{z} = z^{1/2} = \sqrt{r}e^{i\theta/2}.Data said:I gave you the usual definition of the square root function in your other thread. You can use that to figure out what it is.
but if z = x + iy, then r = \sqrt{x^2 + y^2} and \theta = \tan^{-1}\left( y \over x \right)Data said:So let's try out this definition. If z=-1, then we write z = e^{i\pi}, and we get \sqrt{z} = e^{i\pi / 2} = i. As you might expect.
murshid_islam said:what does \sqrt{i^2} equal to? is \sqrt{i^2} = i or \sqrt{i^2} = \pm i?
murshid_islam said:you said, \sqrt{z} = z^{1/2} = \sqrt{r}e^{i\theta/2}.but if z = x + iy, then r = \sqrt{x^2 + y^2} and \theta = \tan^{-1}\left( y \over x \right)