httpswww.0et1.comacceuilattachmentsarticle52c120p1_comlexe 4

⎛−
3 1
2
2 2 i ⎞
= ⎜
−
⎟
⎝
⎠
⎛ ⎛−5π
⎞ ⎛−5π
⎞⎞
= 2 ⎜cos ⎜ ⎟ + i sin⎜ ⎟
6 6
⎟
⎝ ⎝ ⎠ ⎝ ⎠⎠
∀z∈
, arg ≡ −arg z 2
z
* 1
1 1
=
z cos θ + i sinθ
=
cos θ − i sinθ
1
z
=
( θ ) i ( θ )
= cos − + sin −
= [ 1 , −θ
]
⎡ −5π
⎤
= ⎢
2 ,
⎣ 6 ⎥
⎦
[ π ]
[ 1 , θ ]
خاصيات :
نضع :
-1
1 2
∀z∈
, arg ≡ −arg z 2
z
:
* 1
1 2 1 2
( cos θ sin θ ) ( cos α sin α )
z ⋅ z = + i + i
[ ]
arg z ⋅z ≡ arg z + arg z 2 π
[ θ ]
[ α ]
z1 = 1 ,
z2 = 1 ,
[ π ]
( cos θ cos α sin θ sin α) i ( cos θ sin α sin θ cosα)
= − + +
( θ α) i ( θ α)
= cos + + sin +
= [ 1 , θ + α ]
1 2 1 2
[ ]
arg z ⋅z ≡ arg z + arg z 2 π
*
z 2
:
z 1
إذن
لكل
برهان
و
نضع
من
:
:
:
لدينا
إذن
:
-2-
z
1
arg ≡ arg z1 − arg z2
2
z2
:
*
[ π ]
z 2
z 1
‎3‎‏-لكل
برهان
من و
:
arg
z
z
=
⎛
arg z ×
⎝
1 ⎞
⎟
⎠
1
⎜ 1
2
z2
1
= arg z1
+ arg 2
z
2
[ π ]
لدينا :