Thursday, 30 October 2014

Square roots of a complex number



My book says that given the complex number z with modulus r, its square roots are ±reiΘ/2 where Θ is the principal value of argz. My question is that why must we consider the principal value of its argument?


Answer



We consider the principal value by convention. But also if we take the other value θ2+π we find the same two roots because ei(θ2+π)=ei(θ2)


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