![](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 = −0.734158 + 0.668101I
1.43109 − 1.27456I −5.99922 + 4.38526I
u = −0.734158 − 0.668101I
1.43109 + 1.27456I −5.99922 − 4.38526I
u = 0.577379 + 0.799136I
2.16758 + 9.15664I −5.96705 − 5.25155I
u = 0.577379 − 0.799136I
2.16758 − 9.15664I −5.96705 + 5.25155I
u = −0.583021 + 0.792165I
2.76820 − 3.03900I −4.88415 + 0.40129I
u = −0.583021 − 0.792165I
2.76820 + 3.03900I −4.88415 − 0.40129I
u = 0.548606 + 0.780128I
−4.67791 + 4.46553I −11.24364 − 4.14724I
u = 0.548606 − 0.780128I
−4.67791 − 4.46553I −11.24364 + 4.14724I
u = −0.880732 + 0.573012I
−1.06214 + 2.24840I −14.4188 − 2.9053I
u = −0.880732 − 0.573012I
−1.06214 − 2.24840I −14.4188 + 2.9053I
u = 0.908597 + 0.273784I
2.57323 − 5.53278I −10.06397 + 6.98986I
u = 0.908597 − 0.273784I
2.57323 + 5.53278I −10.06397 − 6.98986I
u = 0.814938 + 0.667976I
2.49514 − 2.06773I 0. + 3.71877I
u = 0.814938 − 0.667976I
2.49514 + 2.06773I 0. − 3.71877I
u = −0.887915 + 0.310649I
2.77545 − 0.35472I −9.35777 − 1.48918I
u = −0.887915 − 0.310649I
2.77545 + 0.35472I −9.35777 + 1.48918I
u = −0.551226 + 0.748282I
−1.69458 − 1.28164I −5.29966 + 0.30789I
u = −0.551226 − 0.748282I
−1.69458 + 1.28164I −5.29966 − 0.30789I
u = −0.770088 + 0.744037I
8.45315 − 3.75871I 0. + 2.83567I
u = −0.770088 − 0.744037I
8.45315 + 3.75871I 0. − 2.83567I
u = 0.781202 + 0.741537I
8.62407 − 2.42872I 0
u = 0.781202 − 0.741537I
8.62407 + 2.42872I 0
u = 0.512976 + 0.755043I
−4.91649 − 1.59221I −11.90786 + 3.54404I
u = 0.512976 − 0.755043I
−4.91649 + 1.59221I −11.90786 − 3.54404I
u = 0.886320 + 0.663470I
2.27623 − 3.08946I 0
u = 0.886320 − 0.663470I
2.27623 + 3.08946I 0
u = 1.11340
−7.26377 −11.6170
u = 1.117230 + 0.039150I
−3.19336 − 1.95587I −8.00000 + 0.I
u = 1.117230 − 0.039150I
−3.19336 + 1.95587I −8.00000 + 0.I
u = 0.869584 + 0.106333I
−3.24427 − 2.18605I −17.0727 + 6.0888I
5