![](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 = −0.868634 + 0.432115I
−3.34862 + 4.04370I −6.04453 − 7.13519I
u = −0.868634 − 0.432115I
−3.34862 − 4.04370I −6.04453 + 7.13519I
u = 1.04533
−6.54630 −13.9220
u = −0.026700 + 0.917936I
−14.7670 − 5.6087I −9.35181 + 2.83991I
u = −0.026700 − 0.917936I
−14.7670 + 5.6087I −9.35181 − 2.83991I
u = 0.012118 + 0.901786I
−8.30499 + 2.26267I −6.08064 − 2.91656I
u = 0.012118 − 0.901786I
−8.30499 − 2.26267I −6.08064 + 2.91656I
u = −1.083140 + 0.341712I
−3.37831 + 1.66824I −9.56243 − 0.35146I
u = −1.083140 − 0.341712I
−3.37831 − 1.66824I −9.56243 + 0.35146I
u = 1.076920 + 0.423315I
−2.77345 − 5.10982I −6.71803 + 8.18202I
u = 1.076920 − 0.423315I
−2.77345 + 5.10982I −6.71803 − 8.18202I
u = 0.756512 + 0.350926I
0.83897 − 1.64134I 1.45053 + 5.73960I
u = 0.756512 − 0.350926I
0.83897 + 1.64134I 1.45053 − 5.73960I
u = −0.804096
−1.07276 −10.5910
u = 1.157410 + 0.314330I
−9.45578 + 0.50238I −13.25888 + 0.22265I
u = 1.157410 − 0.314330I
−9.45578 − 0.50238I −13.25888 − 0.22265I
u = −1.110460 + 0.463462I
−8.33031 + 8.05747I −10.74797 − 7.46464I
u = −1.110460 − 0.463462I
−8.33031 − 8.05747I −10.74797 + 7.46464I
u = −0.163704 + 0.669811I
−5.64755 − 3.79286I −7.65510 + 3.79891I
u = −0.163704 − 0.669811I
−5.64755 + 3.79286I −7.65510 − 3.79891I
u = −0.522402 + 0.426932I
−2.44365 − 0.31845I −3.24811 − 0.20471I
u = −0.522402 − 0.426932I
−2.44365 + 0.31845I −3.24811 + 0.20471I
u = −1.267860 + 0.464164I
−12.21500 + 2.58352I −9.43681 − 0.14752I
u = −1.267860 − 0.464164I
−12.21500 − 2.58352I −9.43681 + 0.14752I
u = 1.263650 + 0.477439I
−12.11660 − 7.17755I −9.14770 + 5.86389I
u = 1.263650 − 0.477439I
−12.11660 + 7.17755I −9.14770 − 5.86389I
u = −1.268830 + 0.488464I
−18.5604 + 10.6275I −12.35486 − 5.78214I
u = −1.268830 − 0.488464I
−18.5604 − 10.6275I −12.35486 + 5.78214I
u = 1.280210 + 0.458189I
−18.7882 + 0.7378I −12.72584 + 0.13438I
u = 1.280210 − 0.458189I
−18.7882 − 0.7378I −12.72584 − 0.13438I
5