如何在C＃中计算负数与小数幂？

Question

I am trying to compute negative numbers to fractional power in C#.

This what I tried to compute the power,

Math.Pow(-0.5264, 1.11)--> Result NaN
Math.Pow(-0.5264, 2) --> 0.27709696
Math.Pow(0.5264, 1.11) --> Gives me a result. 

When the base is positive and the power is of fractional i do get a value. But it is failing to give result when base as negative value?

When I tried to find power of a negative base it is returning a complex number format a+bi in matlab.

I really have no clue how to achieve it in C#.

Could someone help me to resolve the issue.

Answer 1

Math.Pow is behaving correctly according to its specification.

If you want the complex value, and you don't have a complex math library, it's easy enough to compute it.

We know Euler's Identity:

e ^ix = cos x + i sin x

and more specifically

e ^iπ = -1

Therefore

0.5264 e ^iπ = -0.5264

Therefore

(0.5264) ^1.11 e ^{1.11 i π} = (-0.5264) ^1.11

Now use Euler's identity again

(0.5264) ^1.11 (cos(1.11 π) + i sin(1.11 π)) = (-0.5264) ^1.11

And so the real part of the number that you're looking for is

(0.5264) ^1.11 cos(1.11 π)

And the imaginary part is

(0.5264) ^1.11 sin(1.11 π)

And now you have reduced the problem to real-valued functions that you can compute with the ordinary math library.

The moral of the story is: solve your math problems by doing mathematics .

Answer 2

You can calculate such expression using System.Numerics.Complex.Pow :

Complex.Pow(-0.5264, 1.11); //(-0,461524987676948, -0,166159219770948)
Complex.Pow(-0.5264, 2).Real; // 0.27709696
Complex.Pow(0.5264, 1.11).Real; // 0.49052441383186784

Usual Math.Pow returns double which is real number not complex.