Given m ∈ R, the complex z = [M (M + 2)] / (m-1) + (m ^ 2 + 2m-3) I, when m is a value, z = (1 / 2) + 4I Parametric equation

Given m ∈ R, the complex z = [M (M + 2)] / (m-1) + (m ^ 2 + 2m-3) I, when m is a value, z = (1 / 2) + 4I Parametric equation

According to the meaning of the question, two equations are obtained
m(m+2)]/(m-1)=1/2；
m^2+2m-3=4;
By solving equation 2
-1+2*2^(1/2)
-1-2*2^(1/2)
Solve one and substitute it into the left side of equation 2 to get 8.5, which is rounded off;
If we solve equation 2, we can get - 1.4, and we can round it off,
So there is no solution to the problem
It is known that M belongs to R, and the complex number Z = m (M + 2) / (m-1) + (m ^ 2 + 2m-1) I. when m is a value, (1) Z belongs to R, (2) Z is an imaginary number, and (3) Z is a pure imaginary number
(1) When Z belongs to R, the imaginary part is equal to 0, that is, m ^ 2 + 2m-1 = 0. Because M-1 is the denominator, M-1 is not equal to 0
(2) When Z is an imaginary number, only m ^ 2 + 2m-1 is not equal to 0 and M-1 is not equal to 0
(3) When Z is a pure imaginary number, the real part is equal to 0, that is, m (M + 2) / (m-1) = 0 and M-1 is not equal to 0
If you need specific results, please let me know
The complex z = m ^ 2-m-6 / M + 3 + (m ^ 2 + 2m-5) I, when m is any value, (1) Z is a pure imaginary number; (2) the corresponding point of Z is above the x-axis
1、
The real part of a pure imaginary number is 0, and the imaginary part is not equal to 0
(m²-m-6)/(m+3)=0
(m-3)(m+2)=0
m=3,m=-2
In this case, the imaginary part M & sup2; + 2m-5 is not equal to 0
So m = 3, M = - 2
2、
Above the real axis, the imaginary part is greater than 0
So M & sup2; + 2m-5 > 0
m-1+√6
Odd function
f(-x)=-f(x)
f(x)+f(-x)=0
ln[(1+ax)/(1+2x)]+ln[(1-ax)/(1-2x)]=0
ln{[(1+ax)/(1+2x)][(1-ax)/(1-2x)]}=0=ln1
[(1+ax)/(1+2x)][(1-ax)/(1-2x)]=1
(1+ax)(1-ax)=(1+2x)(1-2x)
1-A & S... Unfolding
Odd function
f(-x)=-f(x)
f(x)+f(-x)=0
ln[(1+ax)/(1+2x)]+ln[(1-ax)/(1-2x)]=0
ln{[(1+ax)/(1+2x)][(1-ax)/(1-2x)]}=0=ln1
[(1+ax)/(1+2x)][(1-ax)/(1-2x)]=1
(1+ax)(1-ax)=(1+2x)(1-2x)
1-a²x²=1-4x²
So a & sup2; = 4
a≠2
So a = - 2
f(x)=ln[(1-2x)/(1+2x)]
Domain (1-2x) / (1 + 2x) > 0
(1-2x)(1+2x)>0
(2x-1)(2x+1)
What are the greatest common factors of the three prime numbers and their least common multiple 105? What are the three numbers
105 = 3 × 5 × 7. The greatest common factor of the three prime numbers is 1, and their least common multiple is 105. The three prime numbers are 3, 5 and 7 respectively
On the trajectories of complex numbers
In this paper, we give a circle of radius 1 with the point corresponding to complex number 1 + I as the center, and the point Z corresponding to complex number Z as the moving point on the circle, and find the locus of the point determined by w = (1-zi) / (1 + Zi)
I don't know. I suggest rationalizing w first
w=(1-zi)^2/(1+z^2)
=(1+z^2-2zi)/(1+z^2)
Let the circle be (x-1) ^ 2 + (Y-I) ^ 2 = 1
Then the coordinates of Z are:
x=1+sinO
y=i+cos0
The substitution should be about the same
Do adjectives have plural forms in English except for nouns
Are plural forms only nouns? Do adjectives have plural forms? Verbs and adverbs should have absolutely no plural forms
Adjectives have no plural, and pronouns have plural
How to distinguish between such + Adjective + uncountable noun and so + Adjective + uncountable noun?
For example: it's (such / so) good food that we like it very much~
The difference is very simple, the key is to see what the adjective is
2. If the adjective in the structure is "much" or "little", then "so" is used;
If the adjective in the structure is any adjective except "much" and "little", use "such"
3. In the example given by the landlord, the adjective is good, not much / little, so of course use such
He has so much money that he of ten buy some expensive cars
There is so little water in the bottle that we are all thirsty.
It is so good weather today that we would like to go out to play.
I don't think it makes any difference
One is for example, the other is so.
So, of course. It's used to modify adjectives and adverbs.
Such a / an + Adjective + singular countable noun;
So + Adjective + A / an + singular countable noun.
In addition to modifying singular countable nouns, such can also modify plural nouns and uncountable nouns. So is an adverb and modifies adjectives or adverbs.
If plural nouns are preceded by adjectives such as "fee", "many" and uncountable nouns are preceded by adjectives such as "little", "much", so must be used instead of "such"
So, of course. It's used to modify adjectives and adverbs.
Such a / an + Adjective + singular countable noun;
So + Adjective + A / an + singular countable noun.
In addition to modifying singular countable nouns, such can also modify plural nouns and uncountable nouns. So is an adverb and modifies adjectives or adverbs.
If plural nouns are preceded by adjectives such as "feed", "many" and uncountable nouns are preceded by adjectives such as "little", "much", so must be used instead of "such"
The key to the same meaning and different usages and structures lies in the different positions of the indefinite article and the adjective
1such + a (n) + adj + noun 2SO + adj + a (n) + noun, where adj is the abbreviation of adjective
After "such" is generally a countable noun
If met, look at the meaning of the whole sentence, the key word is noun, use such, the key word is emphasis adjective, use so
So + adjectives cannot be followed by uncountable nouns
Fish sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep sheep
Solving complex numbers and finding trajectories
Given z = 1, find the locus of the point corresponding to the complex w = 2Z + 3-4i
Z = a + bi then | Z | & sup2; = A & sup2; + B & sup2; = 1W = 2A + 2bi + 3-4i = (2a + 3) + (2b-4) I so x = 2A + 3Y = 2b-4a = (x-3) / 2B = (y + 4) / 2 so [(x-3) / 2] & sup2; + [(y + 4) / 2] & sup2; = 1 so (x-3) & sup2; + (y + 4) & sup2; = 4
W - (3-4i) = 2Z, so | W - (3-4i) | = | 2Z | = 2 | Z | = 2. Its trajectory is a circle with a distance of 2 from point 3-4i, that is, a circle with a radius of 2 and a center of 3-4i.
English adjectives, singular nouns, plural nouns
There are also American adjectives, singular nouns and plural nouns
English,Englishman,Englishmen
American,American,Americans
British adjectives
Britain
American American
America America
What's the difference between so, such and that?
It is so = it is that?
The difference between "so" and "such" is that "so" modifies adjectives or adverbs, and "such" modifies nouns so that.
”The difference between them lies in the modification of noun singular, such as so + adjective or adverb + A / an + noun singular; such + A / an + adjective or adverb + noun singular
"English teacher team sincerely for you
So + Adjective + A / an + n
Such + A / an + Adjective + n
So... That so that
such...that
So is used to modify adjectives, such is used to modify names, and that is used to modify clauses.
The difference between so and such is so + adj + A / an + n such + A / an + adj + n