Question

What are the real life uses of fourth root of unity?​

Answer 1

Answer:

In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power n. Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, and the discrete Fourier transform.Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity. Any algebraically closed field contains exactly n nth roots of unity, except when n is a multiple of the (positive) characteristic of the field.

Answer 2

Question:

What are the real life uses of fourth root of unity?

Answer:

There are 4 fourth roots of unity and they are

1, i,−1 and−i.The word "unity," perhaps a bit anticlimactically, just means "one." So a root of unity is any number which, when multiplied by itself some number of times, yields 1.1 1 1 and − 1 -1 −1 are the only real roots of unity. If a number is a root of unity, then so is its complex conjugate. The sum of all the k th k^\text{th} kth power of the n th n^\text{th} nth roots of unity is 0 0 0 for all integers k k k such that k k k is not divisible by n .Geometric representation of the 2nd to 6th root of a general complex number in polar form. For the nth root of unity, set r = 1 and φ = 0.When discriminant is equal to zero, the roots are equal and real. When discriminant is less than zero, the roots are imaginary.

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