将单位圆外[tex=2.857x1.357]j+p1FHAeO+ZBvuq0u7R21Q==[/tex]除去线段[tex=3.643x1.357]Vc8aXK1FJhqL17fAKf3LnA==[/tex]与[tex=2.143x1.357]HNhicotwIe09MqHnTMi2nw==[/tex]的区域映为[tex=3.429x1.357]D4tNC4FUoEZdxkuJ5rQLLw==[/tex]的映射.
举一反三
- 求将单位圆外部[tex=2.857x1.357]j+p1FHAeO+ZBvuq0u7R21Q==[/tex]映为全平面除去线段[tex=2.786x1.357]jM7RQ14tFS6f77AbCtta2Q==[/tex]的映射.
- 证明 : 将单位圆内部[tex=2.857x1.357]W2UvKR01GUJgbq0KdXYJYQ==[/tex]映为五角星内部，圆心映为五角星中心的映射为[tex=9.286x3.357]4dphfAmZ2jlKgaI9RGhRXB80yhJB5xPRTFf6FEb2j9aI9BeUbOoM5srNjJ++1JzV4blWef11LtNp6wDX33+dAAQrTj3pzQgf00CxIvzuz68=[/tex]；当五角星外接圆半径为[tex=0.786x1.0]as0RCzgUx1oS48cKHRAVVg==[/tex]时，有[tex=12.214x2.714]XKPofxBZ4i6u8Cfr4jhRPDecW+b4fFEgvqFtvR1TI/KlWjdPg3esyJg06EhxFBIXKAIQ7KjtW7ql6k2ETKc0zoCiP9/p/7a1cUKW0DK+2/4=[/tex].
- 判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]
- 求把单位圆 [tex=2.857x1.357]W2UvKR01GUJgbq0KdXYJYQ==[/tex] 映射成 [tex=3.143x1.357]Sui1bthb4ZFDHMAA/H0Myw==[/tex] 的分式线性映射,并满足条件:[tex=8.643x2.786]4/2fe6ATVmg90LVQ/aOSZzoJXSa1Vdb46Vf+eFRIk+REWcEae/Z7q0IuvDgwq+zO[/tex].
- 分别求将单位圆 [tex=2.857x1.357]W2UvKR01GUJgbq0KdXYJYQ==[/tex] 共形映射成单位圆 [tex=3.143x1.357]Sui1bthb4ZFDHMAA/H0Myw==[/tex] 的分式线性变换 [tex=3.429x1.357]chCZ/z4D0q7yeOcqw4A4Hg==[/tex], 使符合条件:[tex=9.0x2.786]X8eK9FTUblx1D3ueXSlHyFNY9sU7g5zKYFXiCEbfkYTi5e0jJ3BwXYkud5BZzfFQ[/tex]