, ,
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) , , .
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, . .
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, .
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:
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. . , . :
,
( ( ) , , ( ), ).
, , . .