All Precalculus Resources
Example Question #1 : Find The Roots Of Complex Numbers
Evaluate , where is a natural number and is the complex number .
Example Question #2 : Find The Roots Of Complex Numbers
What is the length of
Example Question #3 : Find The Roots Of Complex Numbers
Solve for (there may be more than one solution).
Solving that equation is equivalent to solving the roots of the polynomial .
Clearly, one of roots is 1.
Thus, we can factor the polynomial as
so that we solve for the roots of .
Using the quadratic equation, we solve for roots, which are .
This means the solutions to are
Example Question #4 : Find The Roots Of Complex Numbers
Recall that is just shorthand for when dealing with complex numbers in polar form.
Express in polar form.
First we recognize that we are trying to solve where .
Then we want to convert into polar form using,
Then since De Moivre's theorem states,
if is an integer, we can say