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, ,

x2 = 1.

, , , , .. . , x2 = 1 : x1 = i, x2 = i.

: ii = i2 = 1, ( i)( i) = i2 = 1.

. :

ax2 + bx + c = 0 (a  0),

x , a, b, c , , , a  0. , .

a  0 :

  • , :
  • :
  • :

. , . b2 4ac > 0, . , .

:

, . .

.

1. x2 2x 8 = 0.

. D = b2 4ac = ( 2)2 41( 8) = 36 > 0.

:

2. x2 + 6x + 9 = 0.

. D = 62 419 = 0, :

3. x2 4x + 5 = 0.

. D = 16 415 = 4 < 0, :

, . ( , , ..). VI . , , . . .

, z = x + yi (x, y) , , .

, . .

1 . 2 + 3i A(2, 3) ; 2 3i B(2, 3); 2 + 3i C( 2, 3); 2 3i D( 2; 3). 3i E(0, 3); 3i F(0, 3). , , , , . , x + 0i , 0 + yi, y  0 . Oy , Ox . , (. 2).

, z = x + yi, -: r j Ox Oz (. 3).

r , z, . (. 2) : r2 = x2 + y2 = (x + yi)(x yi) = zz.

() :

z (.. ), . , 1, , 1 (. 4).

 Ox Oz z = x + yi (. 3).

, :  = .

. , , 360. , z (. 3) r, j;  + 360;  + 720;  + 1080;  360;  720;  1080; r , z.

(x; y) z = x + yi. . (. 3):

x = r cos ; y = r sin .

z : z = x + yi = r(cos  + i sin ).

z = r(cos  + i sin ) , z = x + yi, .

:

i r = 1,  = 90, i = 1(cos 90 + i sin 90);

1 r = 1,  = 180, 1 = 1(cos 180 + i sin 180);

1 + i

r = 1,  = 45,

r = 2,  = 120,

. , , , , , r j, :

, .

, :

() (, , ) ( ).

( , , ) , .

.

.

, .

, .

1. ( );

2. , (, , );

3. (1 );

4. , ( , , );

5. . , . :

,

( ( ) , , ( ), ).

, , . .





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