![](data:image/png;base64,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)
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.817592 + 0.566504I
a = 1.001660 + 0.499146I
b = −0.803784 − 0.901222I
−4.82306 + 6.28510I −3.32278 − 7.59393I
u = 0.817592 − 0.566504I
a = 1.001660 − 0.499146I
b = −0.803784 + 0.901222I
−4.82306 − 6.28510I −3.32278 + 7.59393I
u = −0.953679 + 0.230396I
a = 0.530015 + 0.857835I
b = −0.234736 − 1.236490I
0.22966 − 3.35008I 3.44223 + 7.37445I
u = −0.953679 − 0.230396I
a = 0.530015 − 0.857835I
b = −0.234736 + 1.236490I
0.22966 + 3.35008I 3.44223 − 7.37445I
u = 0.867814 + 0.546058I
a = −1.086670 − 0.445288I
b = 0.772557 − 0.231724I
2.45054 + 5.49911I 5.13183 − 6.08008I
u = 0.867814 − 0.546058I
a = −1.086670 + 0.445288I
b = 0.772557 + 0.231724I
2.45054 − 5.49911I 5.13183 + 6.08008I
u = −0.851343 + 0.598329I
a = −0.993809 + 0.234050I
b = 0.744150 − 0.677275I
−0.19697 − 10.34520I 2.00000 + 9.33633I
u = −0.851343 − 0.598329I
a = −0.993809 − 0.234050I
b = 0.744150 + 0.677275I
−0.19697 + 10.34520I 2.00000 − 9.33633I
u = −1.063320 + 0.100601I
a = 0.569690 − 0.407670I
b = 0.152388 + 0.523402I
6.87892 − 1.28336I 11.91682 + 0.I
u = −1.063320 − 0.100601I
a = 0.569690 + 0.407670I
b = 0.152388 − 0.523402I
6.87892 + 1.28336I 11.91682 + 0.I
5