How to decompose the factorial (in complex field) of the polynomial of x minus 1 to the nth power

How to decompose the factorial (in complex field) of the polynomial of x minus 1 to the nth power

x^n=1=cos2π+isin2π
So x = cos (2 π / N) + isin (2 π / N)
n=1,2,3,…… ,n
Get n roots, x1, X2 ,xn
So x ^ n-1 = (x-x1) (x-x2) (x-xn)

Factorization of N-1 of X in complex field
First of all, it's very simple in the complex field, t = 2pi / N, then
What does x ^ n-1 = (x-1) (x-exp (I * t)) (x-exp (I * 2t))... (x-exp (I * (n-1) t)) mean. Exp

Exp is the x power of E!
Look at the picture below!

Factorization of x ^ n-1 in complex number field and real number field
It's mainly the real number field
It's like it's about parity
And COS and sin

Real number field
x^n-1=(x-1)(x^(n-1)+x^(n-2)+..+x2+x1)
Complex field
x^n-1=(x-x1)(x-x2)*...*(x-xn)
xn=cos(2π/n)+ isin(2π/n)

The point on the number axis that represents an integer is called integral point. The unit length of a certain number axis is 1cm. If a line segment AB with length of 2011cm is drawn on the number axis, the number of integral points covered by the line segment AB is ()

The point on the number axis that represents an integer is called integral point. The unit length of a number axis is 1cm. If a line segment AB with 2011cm length is drawn on the number axis, the number of integral points covered by line segment AB is (2011 or 2012)

As shown in the figure, there is an ethnic minority hat. The top part of the hat (including the top and side) is cylindrical, made of black cloth; the brim part is a ring^
As shown in the figure, there is a hat of ethnic minorities. The top part (including the top and side) is cylindrical, made of black cloth; the brim part is a ring, made of white cloth. It is known that the bottom radius, height and brim width of the roof fall are a, so which kind of cloth is used more in black cloth and white cloth?

According to the meaning of the title, I drew one. According to this meaning, black cloth and white cloth use the same amount

A student does a math problem: when x = - 1, find the value of 10x9 + 9x8 + 8x7 + 7x6 + 6X5 + 5X4 + 4x3 + 3x2 + 2x + 1. Because he mistook the "+" sign before an item in the above formula as "-" and got the value of 7 by mistake, which symbol did the student mistakenly read?

Substituting x = - 1 into 10x9 + 9x8 + 8x7 + 7x6 + 6X5 + 5X4 + 4x3 + 3x2 + 2x + 1, we can get - 10 + 9-8 + 7-6 + 5-4 + 3-2 + 1 = - 5. If the value of the algebraic formula is 7 by mistake, which is 12 larger than - 5, then 12 △ 2 = 6, and the coefficient is 6, quintic term. That is to say, the sign of quintic term is wrong

How many natural numbers between 1 and 999 contain the number 3?

Consider the number of 000 to 999:
9 * 9 = 81, a total of 81 * 3 = 243
There are only two 3's in two places: 3 × 9 = 27
There are three in three: one
There are 243 + 27 + 1 = 271
Therefore, there are 271 natural numbers with the number 3 between 1 and 999

The bus and the truck run from a and B at the same time. They meet each other in 5 hours. It is known that the speed ratio of the two cars is 4:5. How many hours does it take for the bus to complete the whole journey?

If the speed of the bus is x and the time is y, then the speed of the train is 5 / 4 X
Y＝（X＋5/4 X）*5 /X
＝45/4 X /X
＝45/4
= 11 1 / 4 (hours)
So the answer is that it takes 11 and 1 / 4 hours for a bus to complete the journey
Add: 5 / 4 is 4 / 5, and so on,

When the function y = (X-2) (3-x) takes the maximum value, x = ()

2.5

How to solve 3x (X-2) + 4 = 7.6 or 3x (x + 2) + 4 = 7.6

3X-6+4=7,6
3x=7.6-4+6
3X=12.6
X=4.2