Question

What are the fourth roots of unity in rectangular and polar form? Solve this problem by creating and solving a
polynomial equation. Show work to support your answer.

Answer 1

Answer:

$\sqrt[4]{1} ={(1,i,-1,-i)$

$\sqrt[4]{1} ={(1\angle0,1\angle90,1\angle180,\angle270)$

Step-by-step explanation:

The polynomial equation that leads to the fourth roots of unity is the following:

$x^4+1=0$

This equation has as solutions the actual roots of the polynom $(x^4+1)$, whose roots are, in fact, the routh roots of unity (unity here is the zero-degree term of the polynom).

In rectangular form, the four solutions (roots) are:

$\sqrt[4]{1} ={(1,i,-1,-i)$

Notice that all of them satisfy the equation $x^4+1=0$.

In polar form ($argument \angle angle$):

$\sqrt[4]{1} ={(1\angle 0 \degree,1\angle90\degree,1\angle180\degree,\angle270\degree)$