MATLAB: 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

MATLAB: 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

complex numbersMATLAB

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.

Best Answer

  • 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.
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