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?

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.

Answer 1

[Steven Lord]

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.