Why do different solutions arise from these seemingly identical approaches to a typing these numbers in? If I exponentiate a number as a variable, it becomes imaginary, if I type in the number directly, it stays rational?

Question

Adam Goldsmith 2017-6-19

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https://ww2.mathworks.cn/matlabcentral/answers/345398-why-do-different-solutions-arise-from-these-seemingly-identical-approaches-to-a-typing-these-numbers

回答： Steven Lord 2017-6-19

采纳的回答： Steven Lord

在 MATLAB Online 中打开

I'm probably wording this poorly, but this isn't making any sense to me.

I have a set of variables that I've defined as:

K = 1.04 - r
rB2 = ((C0 + C1 * ((log(dt) - C2) / (log(1/T(i)) - C3))^(1/C4)) + 1)^-1
rc   = ((rB2 - r)/(1 - r0))^K

r, C0 - C4 are are all real floating constants with no imaginary portion, T is simulated temperature at step i and dt is timestep. rB2 returns a number with no imaginary constant.

For my numbers, as an example, rB2 = 1.3e-33, r = 0.79, and K = 0.25.

((1.3e-33 - 0.79)/(1-0.79)) = -3.7619, and -3.7619^0.25 = -1.3927, right?

....except when it doesn't! Sometimes, MATLAB returns an imaginary number, 0.9848 + 0.9848i, depending on how I type the equation in. For example, here's some command line output:

>> ((rB2 - r)/(1-r))
ans =
     -3.7619
>> ans^K
ans =
     0.9848 + 0.9848i
>> -3.7619^K
ans =
     -1.3927

what the heck?? if I state the number -3.7619 as a variable (any variable, not just 'ans'), it comes out imaginary when exponentiated by K... but not if I type the number in by hand. Also,

>> ((1.3e-33 - 0.79)/(1-0.79))
ans =
     -3.7619
>> ((1.3e-33 - 0.79)/(1-0.79))^0.25
ans =
     0.9848 + 0.9848i

So, what is the difference between these two seemingly identical approaches of typing the numbers in?? And how do I get a script to generate a value rc that isn't imaginary without typing it in myself every iteration of the script?

Thanks in advance.

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Answer 1

Steven Lord 2017-6-19

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https://ww2.mathworks.cn/matlabcentral/answers/345398-why-do-different-solutions-arise-from-these-seemingly-identical-approaches-to-a-typing-these-numbers#answer_271200

在 MATLAB Online 中打开

By operator precedence, the power operator ^ is computed first then the unary minus operator - is applied. So these two expressions are the same:

x1 = -3.7619^K
x2 = -(3.7619^K)

In both those cases, you're raising a positive number to a fractional power which results in a real result then that real result is being negated. If you want to raise the negative number to a power:

x3 = (-3.7619)^K

Raising a negative number to a fractional power can result in a complex number, even when there is a real number that is also a root of the negative number. See the first example in the documentation for the nthroot function for more information.