SOLUTION: I'm having a hard time with complex and real numbers. I know that I^2=-1 and that I=sqrt(1). I don't understand when I is set to a negative power such as I^-1,i^0, or when I is a

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I'm having a hard time with complex and real numbers. I know that I^2=-1 and that I=sqrt(1). I don't understand when I is set to a negative power such as I^-1,i^0, or when I is a       Log On


   

Question 1065494: I'm having a hard time with complex and real numbers. I know that I^2=-1 and that I=sqrt(1). I don't understand when I is set to a negative power such as I^-1,i^0, or when I is a fraction such as 1^37/1^19. thank you for your time
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
To make this short, system%28-1=sqrt%28i%29%2Cor%2C-1=-sqrt%28i%29%29.

Why? .

The definition comes from making i%5E2=-1.

--
Example of a negative power
i%5E%28-2%29
1%2Fi%5E2
1%2F%28-1%29
-1-------negative 1


Another example of a negative power
i%5E%28-3%29
1%2F%28i%5E3%29
1%2F%28i%5E2%2Ai%29
1%2F%28%28-1%29i%29
-1%2Fi
%28-1%2Fi%29%28i%2Fi%29, multiplying entire fraction by 1
%28-i%29%2F%28i%2Ai%29
%28-i%29%2F%28-1%29
i-------positive i