Complex number (2 + I) I / 1-I= Write the answer directly

Complex number (2 + I) I / 1-I= Write the answer directly

The result should be (I-3) / 2

In the range of complex number, factorization x ^ 5-1

X^5-1
=x^5-i^5
=(x-i)(x^4+x^3i+x^2i^2+xi^3+i^4)
=(x-i)(x^4+x^3i-x^2-xi+1)

On the factorization of x ^ 7-1 in the complex range

First, find the seven roots of x ^ 7-1 = 0
X1=1
X2=cos(2PI/7)+i*sin(2PI/7)
X3=cos(4PI/7)+i*sin(4PI/7)
X4=cos(6PI/7)+i*sin(6PI/7)
X5=cos(8PI/7)+i*sin(8PI/7)
X6=cos(10PI/7)+i*sin(10PI/7)
X7=cos(12PI/7)+i*sin(12PI/7)
X^7—1
=(x-X1)*(x-X2)*(X-X3)*(X-X4)*(X-X5)*(X-X6)*(X-X7)
=(X-1)*[X-cos(2PI/7)+i*sin(2PI/7)]*[X-cos(4PI/7)+i*sin(4PI/7)]*[X-cos(6PI/7)+i*sin(6PI/7)]*[X-cos(8PI/7)+i*sin(8PI/7)]*[X-cos(10PI/7)+i*sin(10PI/7)]*[X-cos(12PI/7)+i*sin(12PI/7)]