Given that the complex Z satisfies Z ·. Z + 2I · z = 4 + 2I (where I is an imaginary unit), then the complex Z ·=______ ．

Given that the complex Z satisfies Z ·. Z + 2I · z = 4 + 2I (where I is an imaginary unit), then the complex Z ·=______ ．

Let z = x + Yi, and substitute it into the equation Z ·. Z + 2I · z = 4 + 2I, then we get x2 + Y2 + 2xi-2y = 4 + 2I, so we have x2 + Y2 − 2Y = 42x = 2, then we get x = 1y = − 1 or 3, so & nbsp; Z = 1-I or Z = 1 + 3I, so the answer is: 1-I or 1 + 3I

Given that the imaginary part of the complex Z is 4 and the module of the vector corresponding to the complex Z in the complex plane is 5, we can find the complex Z

Z = 4I + 3 or Z = 4i-3

The greatest common factor of a and B is 12 and the least common multiple is 252

252=2*2*3*3*7
Because B must have the greatest common factor 12 with 36, so B is 2 * 2 * 3 * 7 = 84

In the circuit system diagram, what are the meanings of K1, K2, KK1 and lighting C1, C2, C3, C4 system diagram values are the same, why should they be divided into these

In the circuit system diagram, air conditioner K1 K2 KK1 represents the serial number of air conditioner circuit;
C1, C2, C3 and C4 in the lighting system diagram represent the serial number of lighting circuit;

On English plural pronunciation
How do you pronounce "s" after English and "Z + es" after English

There ~ is ~ a good book in my desk. Can you speak ~ English or French

If the parabola y = ax + 2aX + C intersects the X axis with a, B (a left, b right), and ab = 4, find the coordinates of a, B

∵ a left B right ∵ XB > xay = ax ^ 2 + 2aX + CXA + XB = - 2xaxb = C / AAB = XB XA = √ (XB XA) ^ 2 = √ [(XB + XA) ^ 2-4xaxb] = √ [(- 2) ^ 2-4c / a] = 44-4c / A = 164c / a = 4-16 = - 12C / a = - 3C = - 3a ∵ y = ax ^ 2 + 2ax-3a = a (x + 3) (x-1) ∵ XA = - 3 XB = 1 ∵ a coordinates are (- 3,0) B coordinates are (1

Given a > b > C, M = Ba ^ 2 + CB ^ 2 + AC ^ 2, n = AB ^ 2 + BC ^ 2 + Ca ^ 2, compare the size of M and n

M=ba^2+cb^2+ac^2 = b*a*a+c*b*b+a*c*c
N=ab^2+bc^2+ca^2 = a*b*b+b*c*c+c*a*a
1. Given a > b > C, assume that a, B and C are all positive numbers
Let a = 3, B = 2, C = 1
M=ba^2+cb^2+ac^2 = 2*9+1*4+3*1 = 18+4+3 = 25
N=ab^2+bc^2+ca^2 = 3*4+2*1+1*9 = 12+2+9 = 23
M > N
2. Suppose that a, B and C are all negative numbers
Let a = - 1, B = - 2, C = - 3
M=ba^2+cb^2+ac^2 = (-2)*1+(-3)*4+(-1)*9 = -2-12-9 = -23
N=ab^2+bc^2+ca^2 = (-1)*4+(-2)*9+(-3)*1 = -4-18-3 = -25
M>N
In general, M > n

How to eliminate the parameter of the parametric equation x = 4 + 5cost, y = 5 + 5sint

x-4=5cost,y-5=5sint
(x-4)^2=25cos^2t,(y-5)^2=25sin^2t
(x-4)^2+(y-5)^2=25(cos^2t+sin^2t)
(x-4)^2+(y-5)^2=25
So the image is a circle with (4,5) as the center and radius of 5

Several factorization problems
（X-3)(x-5)+1
（x²+4）²-16x²
(x-2y) cubic-x + 2Y
XY-2, 1 / 2 x - (?) 178; 1 / 2 y - (?) 178;

1、(x-3)(x-5)+1=x^2-8x+16=(x-4)^2 ；
2、(x^2+4)^2-16x^2=[(x^2+4)+4x][(x^2+4)-4x]=(x+2)^2*(x-2)^2 ；
3、(x-2y)^3-x+2y=(x-2y)^3-(x-2y)=(x-2y)*[(x-2y)^2-1]=(x-2y)*(x-2y+1)(x-2y-1) ；
4、xy-1/2*x^2-1/2*y^2= -1/2*(x^2-2xy+y^2)= -1/2*(x-y)^2 .

As shown in the figure, the parabola y = x2-2x-2 intersects the X axis at two points a and B, the vertex is C, and the center of the circle passing through three points a, B and C is m. (1) find the coordinates of the center m; (2) find the length of the inferior arc AB on ⊙ m; (3) whether there is a point D on the parabola, so that the line OC and MD are bisected? If it exists, write the coordinates of point d directly; if not, explain the reason