![](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 = −1.01926
a = 1.09396
b = −2.50941
−7.51678 −13.0910
u = 0.814269 + 0.697849I
a = −0.135222 + 1.183260I
b = −0.021919 − 1.343220I
−3.61218 − 4.89234I −8.33842 + 5.53487I
u = 0.814269 − 0.697849I
a = −0.135222 − 1.183260I
b = −0.021919 + 1.343220I
−3.61218 + 4.89234I −8.33842 − 5.53487I
u = −0.151212 + 0.886118I
a = 0.259000 − 0.151859I
b = 0.317232 + 0.130128I
1.33808 + 1.89910I 2.88769 − 4.28758I
u = −0.151212 − 0.886118I
a = 0.259000 + 0.151859I
b = 0.317232 − 0.130128I
1.33808 − 1.89910I 2.88769 + 4.28758I
u = −0.524511 + 0.603470I
a = 0.421833 − 0.890237I
b = −0.173796 + 0.509907I
−0.23007 + 1.50880I −2.26409 − 4.36176I
u = −0.524511 − 0.603470I
a = 0.421833 + 0.890237I
b = −0.173796 − 0.509907I
−0.23007 − 1.50880I −2.26409 + 4.36176I
u = 0.413009 + 0.524274I
a = 2.66953 + 0.96171I
b = −0.655191 + 0.306962I
−3.04819 + 0.77610I −9.75157 + 2.68802I
u = 0.413009 − 0.524274I
a = 2.66953 − 0.96171I
b = −0.655191 − 0.306962I
−3.04819 − 0.77610I −9.75157 − 2.68802I
u = 0.568174
a = −1.49974
b = −1.19167
−2.38424 −2.38490
5