Complex number when using variables

I am getting two different answers in MATAB 2017a. If I compute it directly in the Command Window vs assigning the variables x,y, I get a complex answer?

-50.8478 ^ -1.017

ans =

-0.0183959070209519

K>> x = -50.8478; y = -1.017

K>> x^y

ans =

-0.0183696777893977 + 0.000982004601423454i

[user86753]

Thanks!

Answer 1

[Steven Lord]

That's correct. The unary minus operator (before 50.8478) is at precedence level 4. The matrix power operator with unary minus (between 50.8478 and 1.017) is at precedence level 3. So:

 -50.8478 ^ -1.017

is equivalent to:

-(50.8478^-1.017)

The expression inside the parentheses is real.

When you use variables:

x = -50.8478;
y = -1.017
x^y

that is equivalent to:

(-50.8478)^(-1.017)

which gives a complex result.

Answer 2

[James Tursa]

Operator precedence

>>  -50.8478 ^ -1.017
ans =
   -0.0184
>> (-50.8478) ^ -1.017
ans =
  -0.0184 + 0.0010i
  

The ^ operator has higher precedence than the - operator when typed in at the command line.