![](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 = −0.223462 + 0.933764I
−0.07570 − 1.69164I 0
u = −0.223462 − 0.933764I
−0.07570 + 1.69164I 0
u = 0.791209 + 0.516161I
10.32730 + 7.27403I 5.32581 − 5.73192I
u = 0.791209 − 0.516161I
10.32730 − 7.27403I 5.32581 + 5.73192I
u = 0.037106 + 1.056750I
−0.19944 − 2.21631I 0
u = 0.037106 − 1.056750I
−0.19944 + 2.21631I 0
u = 0.796662 + 0.503525I
12.03280 − 0.97322I 7.54914 + 0.I
u = 0.796662 − 0.503525I
12.03280 + 0.97322I 7.54914 + 0.I
u = −0.787400 + 0.509956I
7.67805 − 2.34302I 0
u = −0.787400 − 0.509956I
7.67805 + 2.34302I 0
u = 0.543765 + 0.916385I
2.63357 − 1.71163I 0
u = 0.543765 − 0.916385I
2.63357 + 1.71163I 0
u = −0.805009 + 0.474254I
11.86550 + 2.32230I 7.32986 + 0.I
u = −0.805009 − 0.474254I
11.86550 − 2.32230I 7.32986 + 0.I
u = −0.807000 + 0.462064I
10.0185 + 10.5475I 4.83061 − 6.04400I
u = −0.807000 − 0.462064I
10.0185 − 10.5475I 4.83061 + 6.04400I
u = −0.508321 + 0.945367I
0.05765 − 2.39517I 0
u = −0.508321 − 0.945367I
0.05765 + 2.39517I 0
u = 0.801408 + 0.464683I
7.42012 − 5.56366I 0. + 2.51060I
u = 0.801408 − 0.464683I
7.42012 + 5.56366I 0. − 2.51060I
u = 0.308336 + 1.036850I
−3.73977 − 0.08549I 0
u = 0.308336 − 1.036850I
−3.73977 + 0.08549I 0
u = −0.285037 + 1.047880I
−1.75442 + 4.74800I 0
u = −0.285037 − 1.047880I
−1.75442 − 4.74800I 0
u = −0.769820 + 0.487123I
5.19035 − 0.86260I 1.23878 + 3.04762I
u = −0.769820 − 0.487123I
5.19035 + 0.86260I 1.23878 − 3.04762I
u = 0.778145 + 0.470305I
5.09099 − 3.85034I 0.89323 + 3.65261I
u = 0.778145 − 0.470305I
5.09099 + 3.85034I 0.89323 − 3.65261I
u = −0.339809 + 0.830779I
−0.13330 − 1.63331I −0.57375 + 3.86192I
u = −0.339809 − 0.830779I
−0.13330 + 1.63331I −0.57375 − 3.86192I
5