What is the greatest common factor of 4 and 9____ The least common multiple is What is the greatest common factor of 4 and 9____ The least common multiple is

What is the greatest common factor of 4 and 9____ The least common multiple is What is the greatest common factor of 4 and 9____ The least common multiple is

4 = 1x29 = 1x3x3, so the greatest common factor is 1
4 and 9 are coprime, so the least common multiple of 4 and 9 is 9 × 4 = 36
4 and 15 and 9 least common multiple and greatest common factor
Least common multiple 180
Greatest common factor 1
Ask a question about the plural number of senior two
Calculate I + 2I ^ 2 + 3I ^ 3 + 50i^50
Please write down the process
The original formula is i-2-3i + 4 + 5i-6-7i + 8 + 9i - +49i-50
=(-2+4-6+8-10+12-…… +48-50)+i(1-3+5-7…… -47+49)
=2×12-50+i(1+2×12)
=-26+25i
If the complex number (1 + bi) (2 + I) is pure imaginary, what is the value of B?
What are the pronunciation rules of plural words?
When the consonant is voiced, the consonant is voiced
When voiced sounds (voiced consonants and vowels) are received, voiced sounds are produced [Z]
When the consonant (s, Z ∫ 3, t ∫ D3) which is similar to s is used, ES is added and [iz] is issued
When it is followed by T D, it is read as [TS] [DZ]
The rule of plural change
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Case construction method pronunciation example words
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In general, add - S 1. Read after consonant / S /; map maps
2. After voiced consonants and vowels, bag bag... Unfolds
The rule of plural change
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Case construction method pronunciation example words
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In general, add - S 1. Read after consonant / S /; map maps
2. Voiced consonants and bag bags after vowels
Read / Z /; car cars
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S, SH, CH,
The words ending in X and so on are read with - ES / iz / bus buses
watch-watches
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With CE, Se, Ze,
(d) And so on
S / iz / license licenses
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Change the consonant letter + y into I
At the end of the word, add es to read / Z / Baby --- babies
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Irregular changes of plural nouns
1）child---children foot---feet tooth---teeth
mouse---mice man---men woman---women
Note: the plural of a compound word with man and woman is also - men and - women.
For example: an English man, two English men. But German is not a compound word, so the plural form is Germany; Bowman is the surname, and the plural form is the Bowman.
2) Simple complex homomorphism such as:
deer，sheep，fish，Chinese，Japanese
li，jin，yuan，two li，three mu，four jin
But in addition to RMB yuan, Jiao and Fen, US dollar, pound sterling and Franc all have plural forms. For example:
a dollar, two dollars; a meter, two meters
3) Collective nouns, in the singular form, but in the plural.
For example: people, a police, a castle and so on are plural in themselves. We can't say "a people, a police, a castle", but we can say "a people, a police, a castle"
A person, a policeman, a head of Castle, the English, the British, the French, the Chinese, the Japanese, the Swiss and other nouns are used as complex numbers when referring to the general name of the people.
The Chinese people are industrious and brave.
4) Nouns ending with s and still singular, such as:
a. Physics is a singular subject.
b. News is an uncountable noun.
c. The United States, the United Nations shall be regarded as singular.
The United Nations was organized in 1945.
d. The plural titles of books, plays, newspapers and magazines can also be regarded as singular.
"The Arabian Nights" is a very interesting story-book.
It's a very interesting story book.
5) It means something made up of two parts, such as glasses, trousers, clothes
If you want to express a specific number, you should use the quantifiers pair; suit; a pair of glasses; two pairs of trousers
6) In addition, there are also some nouns whose plural sometimes means something special, such as: goods, waters, fish
Case of NOUN
In English, some nouns can add "'s" to indicate all relations. The noun form with this suffix is called the possessive case of the noun, such as a teacher's book. The rules of possessive case are as follows:
1) For example, the boy's bag, men's room and men's room.
2) If the noun has plural suffix - s, just add "'", such as: the workers' struggle.
3) Any noun that can't add "'s" can use the structure of "noun + of + noun" to express all relations, such as the name of the title of the song.
4) When referring to the name of a shop or church or someone's home, the noun possessive often does not appear after the noun possessive, such as the barber's.
5) If two nouns are juxtaposed and have's respectively, it means' respectively '; if there is only one's, it means' jointly'.
For example: John's and Mary's room (two rooms) John and Mary's room (one room)
6) At the end of a compound noun or phrase.
A month or two's absence
Verb third person singular
1、 The change rules and pronunciation rules of the third person singular of verbs
The rules of changing the original form of verbs into the third person singular are similar to the rules of pronunciation. Please observe carefully.
1. Most verbs with "s" at the end of the word are pronounced as [S] after clear consonants and [Z] after voiced consonants and vowels. For example:
①stop－stops [s] ; make－makes [s]
②read－reads [z] ; play－plays [z]
2. If it ends with a consonant letter and "Y", first change "Y" into "I", and then read [iz] with "es"
fly－flies [z]； carry－carries [z]
study－studies [z]; worry－worries
3. Those ending with "s, x, CH, SH" are pronounced [iz] by adding "es" at the end of the word
teach－teaches [iz]; watch－watches [iz]
4. For verbs ending in "O", add "es" and read [Z]
go－goes [z] do－does [z]
When the following verbs become singular, the pronunciation of the vowel part of the original word has changed greatly. Please remember. For example:
1、do [du:]－does [dz]
2、say [sei]－says [sez]
For an open syllable word ending with the silent letter "e", if the ending sound is [S], [Z], add "s" and pronounce the letter "e", which is the same as the added "s"
Read and do [iz] together. For example:
close－closes [iz]
2、 Comparing the similarities and differences of the ending changes of the original words: changing "Y" to "" and double writing the last consonant
Example words:
①baby－babies
②carry－carries
③ Study studying
Ask a plural question
It is known that a solution of quadratic equation with real coefficients is 3 + 2I
The solution of imaginary number with real coefficient is conjugate imaginary number
So the other solution is 3-2i
x²+bx+c=0
Weida theorem
b=-(x1+x2)=-6
c=x1x2=9+4=13
So x & sup2; - 6x + 13 = 0
Because it is a real coefficient equation, two solutions of the equation are conjugate complex numbers, and the other solution is 3-2i
We get X1 + x2 = - 6, x1x2 = 13 by Weida's theorem
So the original equation is x ^ 2-6x + 13 = 0
If the complex number (a ^ 2 + a-6) / (a + 2) + (a ^ 2-5A + 6) I (a ∈ R) is a pure imaginary number, then the value of a is A.3 B. - 3 C.2 or - 3 D.2
(a^2+a-6)/（a+2）=0,a^2-5a+6≠0
So choose B
Choose B, you should face it! That's the answer! Ha ha
Is it necessary to pluralize all words?
no
for example
he has a book
he has many books
A question about the plural
Let the complex number Z1 corresponding to the OA vector and the complex number Z2 corresponding to the OB vector, if Z1 / Z2 = 1 + √ 3 I, find ∠ AOB
(a + bi) / (c + DI) = (a + bi) (c-di) / [(c + DI) (c-di)] = [(AC + BD) + (BC AD) I] / (C ^ 2-D ^ 2I ^ 2) = [(AC + BD) + (BC AD) I] / (C ^ 2 + D ^ 2) take (AC + BD) as a vector multiplied by B vector, and C ^ 2 + D ^ 2 as a module of B vector (AC + BD) / (C ^ 2 + D ^ 2) = 1 is a * B / (b module), but a module I don't
1、 Basic knowledge points——
The argument of complex number: take the positive half axis of X axis as the starting edge, the ray where the vector is located (starting)
The angle θ whose terminal edge is O is called the argument of the complex z = a + bi.
The argument of complex z = a + bi, which is not equal to zero, has infinitely many values with a difference of 2 π
An integral multiple of. The value of the radiation angle θ suitable for [0,2 π] is called the principal value of the radiation angle
Argz, that is, 0 ≤ argz < 2 π.
When a ∈ R +, there is the following relation:
... unfold
1、 Basic knowledge points——
The argument of complex number: take the positive half axis of X axis as the starting edge, the ray where the vector is located (starting)
The angle θ whose terminal edge is O is called the argument of the complex z = a + bi.
The argument of complex z = a + bi, which is not equal to zero, has infinitely many values with a difference of 2 π
An integral multiple of. The value of the radiation angle θ suitable for [0,2 π] is called the principal value of the radiation angle
Argz, that is, 0 ≤ argz < 2 π.
When a ∈ R +, there is the following relation:
arga=0
arg(-a)=π
arg(ai)=
arg(-ai)=π
A necessary and sufficient condition for the equality of complex numbers: every complex number not equal to zero has a unique module and argument
The principal value of the angle. And it can be uniquely determined by the principal value of his module and radiation angle. So two are nonzero
The complex numbers are equal if and only if their modules and the principal values of the argument are equal respectively.
Trigonometric form of complex: any complex z = a + bi can be expressed as R (COS θ)
+Where r = cos θ =, sin θ =, R (COS θ + isin θ)
It is called the trigonometric form of the complex number a + bi. In order to distinguish it from the trigonometric form, a + bi is called the trigonometric form
The algebraic form of the complex number.
Multiplication of complex trigonometric form: multiplication of two complex numbers, the module of the product is equal to the module of each complex number
The argument of the product is equal to the sum of the arguments of the complex numbers
If zriscoin = 1 + 2 (θ s)
Then Z1 * Z2 = R1 (COS θ 1 + isin θ 1) * R2 (COS θ 2 + isin θ 2)
=r1*r2*[cos(θ1+θ2)+isin(θ1+θ2)]
Geometric meaning of complex multiplication: when multiplying two complex numbers Z1 and Z2, you can draw the difference first
The vector corresponding to Z1 and Z2, and then rotate the vector one counter clockwise
Angle θ 2 (if θ 2 ＜ 0, it is necessary to rotate a θ 2 clockwise), and then turn it
If the modulus of Z becomes R2 times of the original, the resulting vector represents the product Z1 * Z2.
Demover's theorem: the module of the n-th power (n ∈ n) of the complex Z is equal to the n-th power of the module of the complex Z
The argument of a power is equal to N times the argument of the complex number
If z = R (COS θ + isin θ)
Zn=[r(cosθ+isinθ)]n=rn(cosnθ+isinnθ)(n∈N)
Division of complex trigonometric form: two complex numbers are equal, and the module of quotient is equal to the module of divisor
The quotient obtained by dividing the modulus of the divisor. The argument of the quotient is equal to the argument of the divisor minus the argument of the divisor
There is a formula for the difference of angle
If Z1 = R1 (COS θ 1 + isin θ 1), Z2 = R2 (COS θ 2 + isin θ 2). )
=[cos(θ1-θ2)+sin(θ1-θ2)]
Root of complex trigonometric form: the n-th root of complex number (n ∈ n) is n complex numbers, they are
All the modules of the complex number are equal to the n-th root of the module of the complex number, and their radiation angles are equal to 0, 1, 2 of 2 π,
... One nth of the sum of (n-1) times.
The n-th root of complex R (COS θ + isin θ) is:
(cos+isin)k=0，1，… (n-1)
Square root of negative real number: if a ∈ R +, then the square root of - A is ± I.
Pairing theorem of imaginary roots for quadratic equations with real coefficients: quadratic equations with real coefficients
The equation AX2 + BX + C = 0 has two roots in the complex set C: x =,
(b2-4ac < 0) obviously they are a pair of conjugate complex numbers. This shows that the real coefficient is one yuan and two yuan
If there is an imaginary root equation,