I.
(x, y) , :
, (1.1)
. (1.2)
z, , z = (x, y). z = (x, y) Re z Im z.
C.
z 1 = (x 1, y 1) z 2 = (x 2, y 2) , x 1 = x 2 1 = 2.
(1.1) (1.2) , z = (x, y)
z = (x, 0) +(0, 1)∙(y, 0). (1.3)
(x, 0) (y, 0) x y, (0, 1) i ( imaginaire ). (1.3) :
. (1.4)
(1.4) . , (1.2) .
.
z 1 = (x 1, y 1) z 2 = (x 2, y 2) :
.
z = (x, y) , | z |. , | z |= .
, , x + iy, , . i : , , , , .
1.1. : .
► , :
.
, , , . , 3 + 4 i, :
.
, : .◄
2. ,
.
. 2.1. |
, . , (, ) . , , , , . , , , . . | z | = r - (. 2.1).
, (2.1)
. z Z . φ , Ox - M ( φ > 0, , φ < 0 ). : , . : .
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(2.1) , z
z , (2.2)
. , φ r , z (. 2.1).
z 1 z 2 :
, .
z 1 z 2 :
, (2.3)
. (2.4)
(2.3) (2.4) :
,
n. , . n - z, (2.2), :
, n N, k = 0, 1, 2,..., n 1. (2.5)
. 2.2. n- |
(2.5) : n- n . ( r), , .. n- (. 2.2).
2.1. , :
►, , , , (0, 0) (π/3; π/3) (. 2.3).
) | ) | ) | ) |
. 2.3. 2.1 |
Re z |
Re z |
. 2.4. 2.2. |
► :
, , (2.5): =
= sinφ cosφ , .
k 0, 1, 2, :
k =0 Þ ,
k =1 Þ ,
k =2 Þ .
, . , .
, , (. 2.4). ◄
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