Friday, January 24, 2014

Did you know that there is a complex number whose cube is 8? Most people forget about complex numbers as a cube root. If someone asks, "What is the cube root of 8 ?",  the majority of people will say 2. But -1 + sqrt(-3) is also the cube root of 8.

Let's verify by cubing -1+sqrt(-3)

(-1 + sqrt(-3))^3 = 1(-1)^3 + 3(-1)^2(sqrt(-3)) + 3(-1)(sqrt(-3)^2) + (sqrt(-3))^3

                          = -1 + 3(3i) - 3(3i)^2 + 3i^2(3i)

                          = -1 + 3(3i) + 9 -3(3i)

                          = 8

So if someone wants to wear #8 on a uniform, they could also be clever and say, "I want to wear number (-1 + sqrt(-3))^3."

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