What are roots of unity?

GrareeCowui

GrareeCowui

Answered question

2022-01-31

What are roots of unity?

Answer & Explanation

lorugb

lorugb

Beginner2022-02-01Added 13 answers

Step 1
A root of unity is a complex number that when raised to some positive integer will return 1.
It is any complex number z which satisfies the following equation:
zn=1
where nN, which is to say that n is a natural number. A natural number is any positive integer: (n=1, 2, 3,). This is sometimes referred to as a counting number and the notation for it is N
For any n, there may be multiple z values that satisfy that equation, and those values comprise the roots of unity for that n.
When n=1
Roots of unity: 1
When n=2
Roots of unity: 1, 1
When n=3
Roots of unity =1, 1+3i2, 13i2
When n=4
Roots of unity =1, i, 1, i

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?