1 Topic by ali_fz (edited by ali_fz 2014-09-03 06:18:35)

Topic: fractional power

Hi
I found a problem in excel calculation, but I surprised when realized that graph has not that mistake and calculates exactly.

The problem is (-2)^(2/3).
It has a answer: 1.58

But when I input =(-2)^(2/3) or =POWER(-2,(2/3)) in MS-Excel, it return #NUM! Error.
We should use this formula: =((-2)^2)^(1/3) OR =((-2)^(1/3))^2 to have a true answer.

But Graph draw a true answer in all above conditions. In other hand it return a point table with imaginary part: -0.7937+1.3747i   

f(x)=(-2)^(2/3)   ===> a line with y=1.58
Evaluation Table output: -0.7937+1.3747i

Re: fractional power

I am not sure why the (-2)^(1/3) works in Excel when (-2)^(2/3) does not. However the reason you see different results in Graph is that there is a cubic root here. A cubic root has 3 solutions. When calculating with real numbers, Graph will always pick the real solution if one exists. When calculating with complex numbers, Graph will pick the one with the smallest angle.

Per default Graph calculates with real numbers when plotting, but uses complex numbers in evaluation and table. The setting for plotting with complex numbers can be found in the Edit|Axes dialog, but you probably do not want to change that.

The setting for evaluations is called  Complex form and can be found in the Edit|Options dialog. The default is Rectangular, but if you change it to Real you will get the result you expect.

Re: fractional power

Thanks for your clear response smile