![](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 = −0.909027 + 0.447242I
0.92869 + 3.49340I 1.60875 − 7.12715I
u = −0.909027 − 0.447242I
0.92869 − 3.49340I 1.60875 + 7.12715I
u = 1.011050 + 0.194989I
−2.03194 − 0.41812I −5.90669 + 0.63067I
u = 1.011050 − 0.194989I
−2.03194 + 0.41812I −5.90669 − 0.63067I
u = 0.836766 + 0.445768I
−0.270561 + 0.850318I −0.462815 + 0.737967I
u = 0.836766 − 0.445768I
−0.270561 − 0.850318I −0.462815 − 0.737967I
u = −1.074180 + 0.167529I
−4.56731 − 3.82886I −9.37121 + 3.42519I
u = −1.074180 − 0.167529I
−4.56731 + 3.82886I −9.37121 − 3.42519I
u = −0.984457 + 0.470779I
−0.06113 + 5.08804I −0.46068 − 6.66773I
u = −0.984457 − 0.470779I
−0.06113 − 5.08804I −0.46068 + 6.66773I
u = −1.075750 + 0.257928I
−5.35579 + 3.64528I −10.51815 − 4.55101I
u = −1.075750 − 0.257928I
−5.35579 − 3.64528I −10.51815 + 4.55101I
u = 1.032300 + 0.426575I
−4.14364 − 2.64621I −7.99299 + 4.07353I
u = 1.032300 − 0.426575I
−4.14364 + 2.64621I −7.99299 − 4.07353I
u = 1.004620 + 0.490092I
−2.26947 − 9.85775I −3.99323 + 10.36767I
u = 1.004620 − 0.490092I
−2.26947 + 9.85775I −3.99323 − 10.36767I
u = 0.060601 + 0.870392I
−7.17725 + 8.76370I −4.62718 − 5.86372I
u = 0.060601 − 0.870392I
−7.17725 − 8.76370I −4.62718 + 5.86372I
u = 0.032672 + 0.871748I
−8.95121 + 0.59562I −7.09212 + 0.32730I
u = 0.032672 − 0.871748I
−8.95121 − 0.59562I −7.09212 − 0.32730I
u = −0.052236 + 0.858648I
−4.58264 − 3.82645I −1.55259 + 2.33220I
u = −0.052236 − 0.858648I
−4.58264 + 3.82645I −1.55259 − 2.33220I
u = 0.821385
−1.34152 −6.99070
u = −0.026625 + 0.803166I
−2.30918 − 2.29408I −0.51230 + 3.47946I
u = −0.026625 − 0.803166I
−2.30918 + 2.29408I −0.51230 − 3.47946I
u = 0.635709 + 0.474037I
0.27984 − 4.75284I 0.98705 + 6.79611I
u = 0.635709 − 0.474037I
0.27984 + 4.75284I 0.98705 − 6.79611I
u = −0.553405 + 0.447723I
1.91457 + 0.33323I 4.99514 − 0.71543I
u = −0.553405 − 0.447723I
1.91457 − 0.33323I 4.99514 + 0.71543I
u = 1.216530 + 0.449635I
−5.95571 − 2.15027I 0
5