Proof of plural number In the complex range, the equation / Z / ^ 2 + [1-I] Z -- [1 + I] z = [5-5i] / [2 + I] [I is an imaginary unit] has no solution

Proof of plural number In the complex range, the equation / Z / ^ 2 + [1-I] Z -- [1 + I] z = [5-5i] / [2 + I] [I is an imaginary unit] has no solution

The original equation is reduced to / Z / ^ 2 + [1-I] Z ^ - [1 + I] z = 1-3i
Let z = x + Yi [x y belongs to R]
Substituting x ^ 2 + y ^ 2-2xi-2yi = 1-3i into the equation
So x ^ 2 + y ^ 2 = 1 (1)
2x+2y=3 (2)
Substitute [2] into [1] to sort out 8x ^ 2-12x + 5 = 0
Der TA = - 16 no solution
So the original equation has no solution in the complex range
Mathematical problems (least common multiple and greatest common factor)
When a class is in line, there are more than 4 people in 20 rows and 20 people in 26 rows. How many people in the class at least?
When a class is in line, there are more than 4 people in 20 rows and 20 people in 26 rows. How many people in the class at least?
(20 + 4) / (26-20) = 4 persons / line
20 * 4 + 4 = 84 people
verification
(84 + 20) / 26 = 4
Meet the requirements
Thirty
Thirty
Related proof of plural number
If Z1 and Z2 satisfy | Z1 + Z2 | = | z1-z2 |, it is proved that (z1 / Z2) 2 must be complex
I'd like to trouble you to talk about the solution
If | Z1 + Z2 | = | z1-z2 |, then the angle between Z1 and Z2 must be right angle
Suppose Z1 = a * e ^ (JW), Z2 = b * e ^ [J (W + 90 degrees)]
Then (z1 / Z2) = (A / b) * e ^ (- J90 degrees)
The minor angle is not 0 or 180, so it must be plural
10. The greatest common factor and the least common multiple of 12 and 15 are urgent!
The greatest common factor is 5
The least common multiple is 60
It is known that the complex number Z satisfies | Z | = 1, and Z is not equal to positive and negative I. It is proved that: (Z + I) / (Z-I) is a pure imaginary number
Let z = x + Yi, so x ^ 2 + y ^ 2 = 1 (Z + I) / (Z-I) = [x + (y + 1) I] / [x + (Y-1) I] = [x + (y + 1) I] [x - (Y-1) I] / [x ^ 2 + (Y-1) ^ 2] denominator is a real number. We only need to prove that the numerator is a pure imaginary number, and denominator = x ^ 2 - (xy-x) I + (XY + x) I + y ^ 2-1 = 2xi
wreac
How to distinguish the least common multiple from the greatest common factor
The problem of finding the greatest common factor is to find several relatively large numbers and a smaller number; the condition of finding the least common multiple is to find a smaller number and a larger number
I don't know if it's clear. It's not easy to explain without examples
A proof of plural number
The module of Z = 1, Z is not equal to positive and negative I, it is proved that Z / (1 + Z) belongs to R
Well, you two downstairs, I didn't type the title just now... Sorry, can you help me to have a look again?
What is the conclusion?
Wrong conclusion
-1=1-2
1=2
z=cosa + isina
z/(1+z)=(cosa + isina)/(1+cosa + isina)
=(cosa + isina)(1+cosa - isina)/[(1 +cosa)^2 - (sina)^2]
Z = cosa + isina, and a does not = k × PI + pi / 2;
z/(1+z)=1-1/(1+z)
=(2+cosa)/2(1+cosa)+isina/2(1+cosa)
It can't be real unless a = k * PI.
What is the difference between the method of finding the greatest common factor and the least common multiple
The greatest common factor is the largest factor shared by these numbers, and the least common multiple is the smallest of these numbers. Just understand the definitions of the two, and remember that one is the smallest and the other is the largest
Let z = 1 + 2 / I, find the imaginary part of (Z square + 3 times the conjugate complex number of Z)
z=1+2/i=1-2i
z²+3z=(1-2i)²+3(1-2i)=-3-4i +3-3i=-7i
The imaginary part of the complex number is 7
z=1-2i
So it's (1-2i) & # + 3 (1 + 2I)
=1-4i-4+3+6i
=2i
So the imaginary part is 2
z=1-2i
Z squared equals - 3-4i
3*z=3-6i
The conjugate appendage of 3 * Z is 3 + 6I
The conjugate complex of Z squared + 3 times Z is - 2I
The imaginary part is - 2
What is the greatest common factor and the least common multiple of 54 and 36
Nine