Question

When performing exponential calculations using a negative number as the base, inconsistent results are returned when using the raw value as opposed to a variable containing the value.

In IRB:

1.9.3p194 :001 > -4.5 ** 0.5
 => -2.1213203435596424 
1.9.3p194 :002 > foo = -4.5
 => -4.5 
1.9.3p194 :003 > foo ** 0.5
 => (1.2989340843532398e-16+2.1213203435596424i) 
1.9.3p194 :004 > (-4.5) ** 0.5
 => (1.2989340843532398e-16+2.1213203435596424i) 

What gives? Obviously the compiler is interpreting -4.5 ** 0.5 as -(4.5 ** 0.5), but why the different behavior when using a variable?

Answer 1

It’s taking the first line as

-(4.5 ** 0.5)

which gives the negative square root of 4.5.
The second equation is equivalent to

(-4.5) ** 0.5

hence the complex answer.