Question

The value of (1 − 1 3 ) 3 equals

Answer 1

Step-by-step explanation:

What is value of (-1) ^(1/3)?

When giving the answer to this question you need to be careful after determining what (-1)^(1/3) is transformed into. If it is a complex number then the value is NOT the complex number but its corresponding MAGNITUDE.

If z = (-1)^(1/3) then z^3 = -1 or z^3 + 1 = 0.

z^3 + 1 = (z^2 - z + 1)(z + 1) = 0 => z = [1 + i√3]/2 or z = [1 - i√3]/2 or z = -1.

The VALUE or MAGNITUDE of z or |z| is 1 for z = -1 not -1 or |z| = 1 for both the expression and its conjugate above. For all cases the value is 1 which should not be a surprise since all the roots of z^3 = -1 are on a unit circle with center at the origin in the Cartesian coordinate/complex plane.

Answer 2

Answer:

7.6923%

Step-by-step explanation:

Now we can see that our fraction is 7.6923076923077/100, which means that 1/13 as a percentage is 7.6923%