- 05 Nov 2012 11:57
#14098206
PoFo ethnic party statistics: http://www.politicsforum.org/forum/viewtopic.php?f=4&t=8&p=14042520#p14042520
That's because cube roots don't have one single result.
Replace (-27) by x there. What you get is x^(-1/3), which is equal to 1/[x^(1/3)], right? That's 1 over the cube root of x:
=
The cube root of -27 is not -3. At least not only -3.
= = =
Now we have to define how much is equal to. To solve that, we need to solve the following equation: , where b is -1 and a is .
The solution of that equation gives us not one, but three complex results:
Depending on how you ask, Google gives you -0.333... as a result, as you were expecting. But that's just one of the possible results.
The ‘i’ you got is from the imaginary portion of the complex number. 0.166666667 - 0.288675135*i is a complex number, equal to what you get using the third result of ‘a’ given here. Only of of those 3 solutions is real (real numbers have only 1 cube root). The other two are complex numbers. In case you are not familiar with the complex set, please take a quick look at this.
There is an explanation here.
Replace (-27) by x there. What you get is x^(-1/3), which is equal to 1/[x^(1/3)], right? That's 1 over the cube root of x:
=
The cube root of -27 is not -3. At least not only -3.
= = =
Now we have to define how much is equal to. To solve that, we need to solve the following equation: , where b is -1 and a is .
The solution of that equation gives us not one, but three complex results:
- First result: a = -1
- Second result: a =
- Third result: a =
Depending on how you ask, Google gives you -0.333... as a result, as you were expecting. But that's just one of the possible results.
The ‘i’ you got is from the imaginary portion of the complex number. 0.166666667 - 0.288675135*i is a complex number, equal to what you get using the third result of ‘a’ given here. Only of of those 3 solutions is real (real numbers have only 1 cube root). The other two are complex numbers. In case you are not familiar with the complex set, please take a quick look at this.
There is an explanation here.
PoFo ethnic party statistics: http://www.politicsforum.org/forum/viewtopic.php?f=4&t=8&p=14042520#p14042520