G is the group of nth roots of unity under complex multiplication Zn is the group of integers represented using exponential notation as e(2pi ix)/n, where x is an integer ranging from 0 to n-1. Consider the function to defined by f(e(2pi ix)/n)=[x]n from G -->Zn.  Chose a prime number, n, between 10 and 99, and using n, prove why the function f(e(2pi ix)/n)=[x]n is operation preserving. Justify your work.

Q: Describe the transformations for f(x) = 4log[- 3(x − 2)] + 1 from its base function.

A: The function .To Find:Describe the transformation of the given function.

Q: Show that 3x2 + log2x2 is Theta(x2). log2x is log base 2 of x.

A: Consider 3x2+log2x2 . It is known that  log2x2<x2, for all x>0. Then, log2x2<3x2 for all…

Q: Let f(x)=4x4+x3+x+1 and g(x)=3x2+2x+3 be two polynomials in Z5[x].  Determine the quotient and…

A:

Q: Find all roots of z(z² + 5x – 25) = 125 and their multiplicity: I = -5 with multiplicity 3 I = -125,…

A: Here we find all roots of    x (x2+5x-25) =125and their multiplicity

Q: Q9. (a) (i) Calculate (2 + i√5)(√5 - i). (ii) Hence verify that (√5 - i) is a root of the equ

A: (a) The given expression is 2+i55-i Multiply the terms in the given expression…

Q: 2. Let k be a complex number and P(x) = 8x³ − 4kx² + (2k+6)x +3. Find all values of k for which P(x)…

A: Given the polynomial  P(x)=8x3−4kx2+(2k+6)x+3 , we need to determine the value(s) of  k  such that…

Q: 2 19) Find the value(s) of k such that A = [13] has an inverse. What is the inverse of A?

A:

Q: Now, from the definition of k(m), given by equation (1.135), we find on setting n = 0, 1, 2, ...,…

A:

Q: If Z1=1-3i , Z2= -2+5i, and Z3= -3-4i, determine the following and express in the form x+yi (a)…

A:

Q: state

A: Consider the translation funtion t(x, r) = x + r Consider the scaling function s(x, c) = cx The…

Q: Given (xi, x2024) Vi = 0,...,n, where x0 = -1, x₁ = 0, x2 = 1, x3 = 2, ..., xn = n = 1. Write down…

A: (a). When n=1, we have to points: (x0​,x02024​)=(−1,1) and (x1​,x12024​)=(0,0).  The interpolating…