How to get (-8)^0.333333 = -2 in MATLAB?

Question

Using MATLAB exponential function:

(-8)^0.333333
ans = 1.0000 + 1.7320i

How to get (-8)^0.333333 = -2 instead?

x=-10:-1;
x.^0.333333

How to get real value?

How to redefine ^:

x.^y

to

sign(x).*abs(x.^y))

You probably want to read about this: http://en.wikipedia.org/wiki/Principal_branch — jason, Sep 28 '11 at 02:14

score 4 · Answer 1 · answered Sep 28 '11 at 02:10

4

There are 3 possible answers for the cube root of -8: -2, 1+/- sqrt(3)

You probably want nthroot(-8,3) --> -2

answered Sep 28 '11 at 02:10

Foo Bah

score 3 · Accepted Answer · answered Sep 28 '11 at 02:12

3

MATLAB 7.0 provides the NTHROOT function, which returns the real roots of a number. So your formula becomes NTHROOT(-8, 3) = -2

If you are using a version prior to MATLAB 7.0 (R14), please read the following:

To obtain the real cube root of a negative real number "x", rather than executing:

x.^(1/3)

use the command:

sign(x).*abs(x.^(1/3))

This will find the absolute value of the root and modify it by the sign of the argument.

answered Sep 28 '11 at 02:12

evgeny

Thank you very much. How to redefine ^: x.^(1/3) to sign(x).*abs(x.^(1/3)) – h02h001 Sep 28 '11 at 02:30

2 Answers2