MATLAB: Matlab return me a complex number

complex returns

Hi, Why >>(-27)^(1/3) return me a complex number rather than -3??? I am curious about this. Please help.

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From the documentation

doc power

"Note that for a negative value X and a non-integer value Y, if the abs(Y) is less than one, the power function returns the complex roots. To obtain the remaining real roots, use the nthroot function."

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MATLAB: Why does similar code generate complex numbers

When x is negative, x^n is defined by MATLAB as exp(n*log(x)) . log(x) when x is negative, is log(-x) + pi * 1i . n times that is n*log(-x) + n*pi*1i . exp() of that is going to be complex except when n is an integer (in which case n*pi becomes an exact multiple of pi)

Thus for x negative, f2 = x .^ (1/3); is going to be exp(log(-x)/3 + pi/3*1i) which is going to be complex valued.

nthroot() is defined in terms of real roots, with it being an error for the value to be negative and the power to not be an odd integer.

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