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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.

User Snowindy
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1 Answer

1 vote

Answer:


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


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

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)

User Eyescream
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