3as math sci corrections2

8/13/2019 3as Math Sci Corrections2

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ww.science-collector.com/vb


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:/

: . : . : :/ : . : . : :/ : . : . : : .

:/ : . : . : :/ : . : . :



3/19

.

(((( ))))

; ;O u v

.

1 .A + =1 2a i z

M A 1 2z i= .M A 1 2z i= M A 1 2z i= +.M A 2z i= .

2 .1 2 4z i= 2 3z i= +3 3 3z i= 4 5

2z i=.

3 .ABCD 2 i +1 4i +3 2i+2 i.

( ) ( )1 4 2 1 3B Az z i i i = + + = +( ) ( )3 2 2 1 3C Dz z i i i = + = + B A C D

z z z z = AB DC= A BCD .4 .

Az,

Bz

Cz

Dz ( )3 ;1A( )3; 1B ( )0;2C

( )3 ;3D =.1(4 2Az = =,2Bz =2Cz .= A,BC O 2.2(2 2D AAD z z i= = =,3 2D CCD z z i= = + =

2A O OC CD DA= = = . AOCD= z r .z r =( )Arg z = +.z r=( )A rg z = .

1 1 1

z z r= =

1A rg

z

=

.

7

6

19

30

37



4/19

33 3z z r= =( )3 3A rg z =.

1 1 1 1nn nnz rz z

= = =

( ) ( )1 nnA rg A rg z nA rg z nz

= = =

5 .1

2 2cos sin

2 2 4 4z i i

= + = +.

2

2 2 3 3cos sin

2 2 4 4z i i

= + = +.

3

2 2 3 3cos sin

2 2 4 4z i i

= = + .

1

3 1cos sin

2 2 6 6z i i

= + = +2

3 1 5 5cos sin

2 2 6 6z i i

= + = +

3

1 3cos sin

2 2 3 3z i i

= = + 4 1 3 2 2cos sin

2 2 3 3z i i

= = + .

( )1 3 3 cos 0 sin 0z i= = +( )2 5 5 cos sinz i = = +3 cos sin

2 2z i i

= = +4

1 1cos sin

2 2 2 2z i i

= = +

5 7 7 cos sin2 2

z i i

= = +

.

z x= 0x < ( )cos0 sin0z x i= + 0x > ( )cos sinz x i = +.z yi= 0y < cos sin

2 2z y i

= +

0y > cos sin

2 2z y i

= +

.

1

2 21 2 2 cos sin

2 2 4 4z i i i

= + = + = +

2

2 23 3 3 2 3 2 cos sin

2 2 4 4z i i i

= = = +

3

1 3 2 25 15 2 5 2 5 cos sin

2 2 3 3

z i i i

= = = +

4

3 1 5 56 2 2 2 2 2 cos sin

2 2 6 6z i i i

= + = + = +

.

4 4

1 3

iZ

i

+=

4 41 3

iZ

i

+=

.

1(( )( )

( )4 4 1 34 4

1 3 1 341 3

i iiZ i

i

+ ++= = = + +

.

41

42

43

44

46



5/19

2(

4 2 cos sin5 54 4

2 2 cos sin12 12

2 cos sin6 6

i

Z i

i

+

= = +

+

.

3(1 1 5 5

cos sin12 122 2

iZ

= +

( )

20092009

2 2 cos sin12 12

Z i

= +

5 5

2 2 cos sin12 12

Z i

= +

.

6 .42

i

Az e

= 2AOA z= =( )4

AArg z

=.

23

2

i

Bz e

= 32

BOB z= =( )

2B

Arg z

=.

iCz e

= 1COC z= =( )CArg z =.5

62i

Dz e

= 2DOD z= =( ) 56

DA rg z

= .

3

4 3 3 2 2

6 6 cos 6 3 2 3 24 4 2 2

i

e isin i i

= + = + = +

.

3

2 3 3

5 5 cos 52 2

i

e isin i

= + =

.

( )1 1 1

cos

2 2 2

ie isin

= + = .

2

3 2 2 1 3

2 3 2 3 cos 2 3 3 33 3 2 2

i

e isin i i

= + = = .

7 .22 6 5 0z z + =2' 1 i = '3=

2

iz

=3"

2

iz

+=.

2 3 0z = + 2 23z i= 3z i=3z i= .1 2

1 2

5

2

z z

z z

=

+ = 1z2z 2 2 5 0z z+ + =.

48

49

56

A

O

B

C

D

0 1

1

x

y

A

O

B

C

D

58



6/19



7/19

:/

: . : " ." : :/ : . : " ." : :/ : . : " ." : .

+ ='z az b :/ : . : .

: :/ : . : . :



8/19

:/ : . : . :

.

1 .2(

" " " " " "3

A B B C C A

AB BC CA= = =.

2(" " " " " "

2A B B C C A

AB BC CA= = =.

1(' ' 2M N MN=.

)2 ( )1 4z i z= + + 4z i= .A3(

'2

AM

A M=( ) ( ); ' arg 1

4AM A M i

= + =

.

)4 ' ' ' ' ' ' 2B C B D C DBC BD CD

= = = BCD' ' 'B C D .2 .

)1 22

A K

A B=

4

.

)2 2 4

.

)3 2 4

.

1(3

2

6

.2(

3

3

2

.3(

2

3

6

.4(

1

2

3

.

3 .2(

9 9 3 6 3 5 3 3 10'

2 2 2 2z i z i

+ = + +

.

T ( )' 1z i z i= + ( )1 4

2.

10

11

17

16

1

2

5



9/19

5 . 1S

2

3

.( )S A C= . OCD OA B S . 1S O 2

3

.

.1 .

1(( )0A( )8 8C i+( )4 4P i+( )4 8Q i+.

2(( )1

1

4

= +0 =.

3(2

4 =

4

=.

4(( )16

1 25

i = +

3 .)1 3 9

4z iz i= +.

.=( )A O=( )O B)21. 0O A = C ( )1 2f C = C( )f = 2 C ) ) ( )O A ( ) ( )O B ( )A ( )B ( ) ( )O A B

O .( )AB ( )f A O=( )f O B=( )f = O A

B O

=

2A B O = .

35

26

50



10/19



11/19

:

. :

. :

. :

. .

: .

: .

)1())2 2( 1) 0k k kk G A k G B k G C + + = )2 1) ( )kk G A k BA A C + =

(2( 1 kk G A k BC + = 2 1k kG A BC k= +

3(1 1MG MG =

)E( [ ]1 1G G 4(12 2 2MG MA MB MC MC= +

12 2MG MC=

1G C=

)F( 1G =1R G C5((1 2 1(0;0;8) ; (0;0;2) ; (0;0;0)G G G

1 1 3 302

G GR = = ))F))E

) 2 2 2

( ) : 4

( ) : 30

E z

F x y z

=

+ + =)2 2 ) : 26C x y+ =

)2(:I(1( G { }( ;1);( ;1);( ;3)O A C 3 0GO GA GC + + =



12/19

5GC AC OC = + 5 2GC A j OJ JC = + + 0A j OJ+ = 5 2GC JC = 5 ;.. .2.GC JC .

2(1 3

; ;05 5

G

II(1(3 5MO MA MC MG+ + =

2(( )3 . 0MO MA MC MB+ + =

MG MB= )E( ]]GB

4

1

2

A B

13

4

AC

. 4 ( 1) ( 1)(3) (2)( 4) 15A B A C = + + = 2 2 24 ( 1) 2 21AB = + + =26A C =

. 15cos 0,6419546.

A B A CBA C

A B A C

= =

0130BA C .

) ; ; )M x y z )P ) ( )M P . 0AM u = = +:2 7 0x z))P . ( 1;2;1)n))P

)P(:2 2 0x y z + + =)1 A )p()q( 5

6

)2 M )p()q: ( :2 2

6 6

x y z x y z+ += 2 2x y z x y z+ = +

3 0x z+ = = +2 3 0x y z

13

14

30

2



13/19



14/19

:

.

: d .

: . . )1(I( A( 1 ; 2 ; 2 )B( 3 ; 2 ; 1 )C( 1 ; 3 ; 3 )

)1 ABAC ABA C

2( 1p2p (2;0; 1)u . 0AM u = k 0k. 0M

( ) A ( ) 0A M A ( ).

)2: (1(( .........3( ) : 0

15 5

x t

AB y t

z t

=

=

= +

(y = z = 0 t = - 3 ( E( 9 ; 0 ; 0(30

5

A B

320

10

AC

A BA C

)1 1 1

2

n

8



15/19

2(.........

4

( ) : 2

1 2

x t

D y t t

z t

= +

=

= +

3(H ))D))P ( 4 + t ) ( -2 t ) + 2 ( 1 + 2t ) = 0 43t =

8 2 5; ;

3 3 3H

=( ; )d A u '(2;1;1)u(3;3;0)A ( ; )d B v= (3;1;3)B(1;2; 1)u A B u v = +

2 02 23

+ =

+ =

=

1 23 2

=

=

=

.

: 3 2

3

3 '

1 2 '

3 '

x t

y t

z t

x t

y t

z t

= +

= + =

= + = +

=

3 2

3

3 '

' 6

' 5

x t

y t

z t

t t

t

t

= +

= + =

= =

=

1( an bc

. 0

. 0

n A B

n A C

=

=

1

2

2

A B

23

1

AC

2 2 02 3 0

a b c

a b c

+ + =

+ + =

4

3

1

3

a b

c b

=

=

431

n

( M( x ; y ; z )2 . 0A M n = )4 1) 3( 1) ( 1) 0x y z + + + + = ( ) : 4 3 0P x y z+ + =1( A . 0AB A C =

2( ))P1

1

1

n

3AB n=

)p( ))AB3(( ') : 0A P ax by cz d + + + =3 2 2d a b c= +

3

57

13



16/19

( ')P A C ( ')P 'a

n b

c

A C

) ') : 0P x z =4(

3 0

0

x y z

x z

+ + =

=

2 3

x z

y z

=

= + .........3 2x ty t t

z t

==

=

II(1(D( 0 ; 4 ; - 1 )

3

6

3

AD

ABC1 2

1

n

3AD n= ( ) ( ')A D P2(

127

3

AB CV S A D= =



17/19



18/19

:

. :

:

. .

: .

: :

)1( /

)2: ( .

.

)1 2 2 2y z R+ = A 2 2 13y z+ =)2 )C(1( ) : 2p x = 13. )C(1( ) : 3p y = ( );o i.

)C(1( ) : 4p z = .

1( ( ) ........2

0 .

x t

y tz t

=

= =

)C( 2 2 2 2x y k z+ = 2k )C( )D( )C( )D(

1t = ((2;0; 1 2 4k = 2 2 24x y z+ =

2(( 2 2 24x y zz a

+ =

= 2 2 24x y a+ =24 4a = 1a =

5

7



19/19


3as math sci corrections2

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