-
176
ไพ้ก 85 | w=z+a
w=zใฎ่กจใๅณๅฝข
็นzใๅ็นใไธญๅฟใจใใๅๅพrใฎๅไธใๅใใจใ, w=z+ (a>0) ใๆบใใ
aยฒ
Z
็นwใๆใๅณๅฝขใซใคใใฆ่ใใใ
(1)a=r ใฎใจใ,็นwใฏใฉใฎใใใชๅณๅฝขใๆใใใ
(2) w=x+yi (x, yใฏๅฎๆฐ) ใจใใใ a<r ใฎใจใ, ็นwใๆใๅณๅฝขใฎๅผใx,y
ใ็จใใฆ่กจใใ
ใใ ใใ
ๅค
ๆฌ้ใงใฏ,(2), ใw=x+yi ใจใใใ ใจใใใใ, zใๆฅตๅฝขๅผใง่กจใใฆ่ใใใ
(2)zใๆฅตๅฝขๅผใง่กจใใใจใซใใ,x,yใฏ0ใ็จใใฆ่กจใใใใฎใง,ใคใชใใฎๆๅญใ
ๆถๅปใใฆ,x,yใ ใใฎ้ขไฟๅผใๅฐใใใใฎใใใซ sin20+cos20=1 ใๅฉ็จใใใ
w=z+ =r(coso+isin0)+ (cos 0-isine)
่งฃ็ญ z=r(cos0+isine) (r>0,0โฆ0<2) ใจใใใจ
aยฒ
aยฒ
17 = (r+ aยฒ ) cos 0+i (rโ aยฒ) sine
r
| (1) |z=r2 ใใ
Z
1/2=732 ใงใใใใ
Z
w=z+
aยฒ
72
Z
r
(1) ฮฑ=r ใฎใจใ,โ ใใ w=2a cos 0
Cos91ใงใใใใ
โ ใช
ใใฃใฆ, ฮฑ=r ใฎใจใ
w=z+z
JS
ใจใใใใจใใงใใใ
0โฆ0<2ใงใฏ-1โฆcosโฆ1 ใงใใใใ-2aโฆwโฆ2a
ใใฃใฆ, ็นwใฏ2็น-2a,2a ใ็ตใถ็ทๅใๆใใ
(2) w=x+yi ใจใใใจใ โ ใใ
PT
2
aยฒยฒ
x=(7+ aยฒ ) coso, y = (rโ a) sinฤ
sin20+cos20=1ใซใใ0ใๆถๅปใใใจ, a<rใใ
1J
22
a
+
r
+
2
aยฒ
r
2
=1(ๆฅๅ)
ๅคง
<<a<rใงใใใใ
r-
aยฒ = rยฒ-aยฒ >0
=
or r
ใใค