Free Algebra Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Powers of Complex Numbers

## Positive Whole Number Powers

As an application of the rule for multiplying together complex numbers in polar form, it is a simple matter to multiply a complex number by itself any desired number of times.

Suppose that Then, and, by continuing this process, This result is due to De Moivre, but other aspects of it will need to be discussed before we may formalise what is called â€œDe Moivreâ€™s Theoremâ€.

Example ## Negative Whole Number Powers

If n is a negative whole number, we shall suppose that n = −m, where m is a positive whole number.

Thus, if then In more detail, giving But −m = n, and so showing that the result of the previous section remains true for negative whole number powers.

Example All Right Reserved. Copyright 2005-2022