Math/ imaginary numbers

[allintuit]

How can you evaluate (-4)^(3/2)? I have two possible answers, which seems unusual.

[sweetjazz]

Nothing unusual here -- every complex number (besides zero) has two square roots. Since (-4)^3 = -64, the two values of (-4)^(3/2) are 8i and -8i.

It's nothing different than the fact that there are two square roots of 2: 2^(1/2) and -(2^(1/2)). When taking the square root of a positive real number, we can always pick the positive one if we like. When taking the square root of a complex number, neither one is positive or negative, so each square root is as good as the other.

Hope that helps.

[henrikrh]

DAmn thought I was in OOT and this was gonna be about Calvin and Hobbes.

Eleventeen and twentytwelve, you know.