![](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 = 0.932207 + 0.261463I
−1.57798 − 1.00473I −1.82896 + 0.57498I
u = 0.932207 − 0.261463I
−1.57798 + 1.00473I −1.82896 − 0.57498I
u = −0.963114 + 0.429790I
−0.36195 + 3.85582I 3.97718 − 7.89236I
u = −0.963114 − 0.429790I
−0.36195 − 3.85582I 3.97718 + 7.89236I
u = 0.051158 + 0.880772I
−10.59630 + 5.33673I −1.16942 − 2.96646I
u = 0.051158 − 0.880772I
−10.59630 − 5.33673I −1.16942 + 2.96646I
u = −1.098980 + 0.206450I
−7.37246 − 0.32949I −5.60033 − 0.20899I
u = −1.098980 − 0.206450I
−7.37246 + 0.32949I −5.60033 + 0.20899I
u = 1.030410 + 0.480033I
−5.39158 − 6.75127I −1.33497 + 7.43906I
u = 1.030410 − 0.480033I
−5.39158 + 6.75127I −1.33497 − 7.43906I
u = 0.720594 + 0.453573I
−2.18139 − 1.93104I 3.25405 + 4.18474I
u = 0.720594 − 0.453573I
−2.18139 + 1.93104I 3.25405 − 4.18474I
u = −0.027215 + 0.843903I
−4.30846 − 2.13264I 2.18965 + 3.16032I
u = −0.027215 − 0.843903I
−4.30846 + 2.13264I 2.18965 − 3.16032I
u = 1.237150 + 0.448499I
−8.09804 − 2.43962I −1.44223 + 0.17519I
u = 1.237150 − 0.448499I
−8.09804 + 2.43962I −1.44223 − 0.17519I
u = −1.232480 + 0.474736I
−7.90858 + 6.86486I −0.85861 − 6.16378I
u = −1.232480 − 0.474736I
−7.90858 − 6.86486I −0.85861 + 6.16378I
u = −1.260650 + 0.436852I
−14.6036 − 0.7042I −4.80376 − 0.14810I
u = −1.260650 − 0.436852I
−14.6036 + 0.7042I −4.80376 + 0.14810I
u = 0.311125 + 0.584230I
−3.40769 + 2.56217I 2.05300 − 2.97329I
u = 0.311125 − 0.584230I
−3.40769 − 2.56217I 2.05300 + 2.97329I
u = 1.244860 + 0.491994I
−14.1992 − 10.2647I −4.13372 + 5.98641I
u = 1.244860 − 0.491994I
−14.1992 + 10.2647I −4.13372 − 5.98641I
u = −0.445071 + 0.389205I
1.050410 − 0.215716I 9.69812 + 1.13318I
u = −0.445071 − 0.389205I
1.050410 + 0.215716I 9.69812 − 1.13318I
5