conjugate
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The Theorem says… if a polynomial f(x) of degree n>1 has real coefficients and if z=a + bi with b not= 0 is a complex zero of f(x), then the conjugate of z=a-bi is also a zero of f(x)
You will find it easy to first prove this
LEMMA. If f(x) has real coefficients and if A is a complex number, then
conj(f(A)) = f(conj(A)).
Proof. Let f(x) = a_nx^n + a_(n-1)x^(n-1) + … + a_1x + a_0, where the a’s are real.
Now f(A) = a_nA^n + … + a_1A + a_0, and
conj(f(A)) = conj(a_nA^n) + … + conj(a_1A) + conj (a_0) =
a_n*conj(A^n) + … + a_1*conj(A) + a_0 =
a_n*(conj(A)^n) + … + a_1*conj(A) + a_0 = f(conj(A)).
Now back to your theorem. Let A = a + bi, and suppose A is a root of f(x). Then f(A) = 0. By the lemma, conj(f(A)) = conj(0) = 0, so f(conj(A)) = conj(f(A)) = 0.
Written by rob on December 29th, 2009 with 1 comment.
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The Theorem says… if a polynomial f(x) of degree n>1 has real coefficients and if z=a + bi with b not= 0 is a complex zero of f(x), then the conjugate of z=a-bi is also a zero of f(x)
You will find it easy to first prove this
LEMMA. If f(x) has real coefficients and if A is a complex number, then
conj(f(A)) = f(conj(A)).
Proof. Let f(x) = a_nx^n + a_(n-1)x^(n-1) + … + a_1x + a_0, where the a’s are real.
Now f(A) = a_nA^n + … + a_1A + a_0, and
conj(f(A)) = conj(a_nA^n) + … + conj(a_1A) + conj (a_0) =
a_n*conj(A^n) + … + a_1*conj(A) + a_0 =
a_n*(conj(A)^n) + … + a_1*conj(A) + a_0 = f(conj(A)).
Now back to your theorem. Let A = a + bi, and suppose A is a root of f(x). Then f(A) = 0. By the lemma, conj(f(A)) = conj(0) = 0, so f(conj(A)) = conj(f(A)) = 0.
Written by rob on December 26th, 2009 with no comments.
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I know what "asistir" means(to attend). What does the "a" do at the end and how do you conjugate that?
(yo, tu, el/ella/Ud., nosotros, and ellos/ellas/Uds.?)
AS AN INTRANSITIVE VERB:
asistir = attend
asistir a = attend
"A" is a preposition, equivalent to the English preposition "to". And just like in English, our prepositions don’t change with conjugation. The addition of "a" is necessary TO CONNECT THE DIRECT OBJECT and does not change the meaning of the word.
WRONG: Asistimos un curso de primeros auxilios.
CORRECT: Asistimos a un curso de primeros auxilios.
(We attended a first aid course).
EXAMPLES THAT ILLUSTRATE HOW "A" DOESN’T CHANGE WITH CONJUGATION:
(Yo) Fuí A un evento cultural.
[I went TO a cultural event]
(Tú) Fuiste A un evento cultural.
[You went TO a cultural event]
(Nosotros) Iremos A un evento cultural.
[We are going TO a cultural event]
=======================
AS A TRANSITIVE VERB:
asistir = help, assist
asistir a = help, assist
Here, "a" is necessary to CONNECT THE INDIRECT OBJECT.
Example:
El paramédico asistió a la accidentada.
(The paramedic attended to the accident victim)
Written by rob on December 21st, 2009 with 2 comments.
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How do you conjugate the spanish word estudiaramos in the present tense?
Estudiamos
Written by rob on December 15th, 2009 with 4 comments.
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Explain the relationship between the strength of an acid and its conjugate base and its conjugate acid?
if the base is strong then is conjugate acid is weak and if the base is weak then conjugate acid strong…similarly in the case of acids also!
Written by rob on December 13th, 2009 with 1 comment.
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F+’s have tra genes
That code for sex pili
That plasmid DNA
Passes through
But F+ need F-
As well as 20 genes
And F plasmids too
I wanna conjugate with you
We don’t need Barry White
‘Cos we’ve got tra genes that’s right
Don’t worry about orientation
I can insert F plasmid at different Locations
What a transformation
I hope you appreciate
We can conjugate
Appreciate
Conjugation for the nation
E.coli nation
And stytomycoin (Crap spelling)
Can’t break us apart
‘Cos my res genes
Are the keys to your heart
And when Ampicillin
Tries to break through
You’ll be glad
Oh so glad, I conjugated with you
CHORUS
But I’m an F+
I need about 20 genes
That are necessary to code for
Sex pili assembly
But now that the act is done
It saddens me
You can conjugate with anyone
CHORUS
That’s the way it goes
Species evolution
I gave you something special
Conjugation revolution
F- you get naked
‘Cos you’re my recepient
You must be competent
Conjugation for the nation
E.coli nation
Conjugation
E.coli nation
Copyright 2008 Sian Cook
Duration : 0:3:53
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Technorati Tags: alternative, Cook, indie, midnight667, Sian, singer, songwriter, suffolk, Unsigned
Written by rob on December 12th, 2009 with 2 comments.
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Hola 
I need a little help getting started here. I need to conjugate this sentence based on my wish or reaction. I don’t know where to start, so if someone could conjugate and explain that would be incredible. Gracias.
Diego estuvo dos semanas en un hotel de lujo. (Me alegré de)
Use the subjunctive since it’s your emotion.
Me alegré de que Diego pase dos semanas en un hotel de lujo.
I changed the verb estar to pasar, because you don’t say "is two weeks."
Written by rob on December 10th, 2009 with 2 comments.
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This behavior of the triple conjugates of blepharisma I haven’t figured out. It could possible be that this could be during the later stages of the process.
Duration : 0:2:21
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Technorati Tags: blepharisma, conjugation, protozoa
Written by rob on December 9th, 2009 with 1 comment.
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This is a movie we made for Spanish where we switched the original lyrics to the songs to lyrics that had something to do with conjugation.
We hope you like the video. If you would like to learn more about Spanish Conjugation, please ask your Spanish teacher. ^_^
****NOTE*****
When we use the word conjugate, we used the word in the form of conjugation, just shorter. We did not mean to use the word as something innapropriate. We did not know that it meant something else until one of our mothers told us…. thank you.
Duration : 0:4:48
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Technorati Tags: Bob, conjugation, español, Gaga, Katy, Lady, Marley, music, Perry, Smith, spanish, Videos, Will
Written by rob on December 5th, 2009 with 6 comments.
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A short introduction to Complex Numbers.
Check out www.gaussianmath.com for related math topics and more AMC problems.
Duration : 0:9:22
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Technorati Tags: complex, donny, math, numbers
Written by rob on December 1st, 2009 with 5 comments.
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