![](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 = −1.04049
a = 0.567340
b = −1.20452
0.339162 13.0620
u = −0.748785 + 0.823629I
a = 0.412890 − 0.456902I
b = 0.679306 + 1.137690I
6.90977 − 8.77559I 9.73876 + 7.09449I
u = −0.748785 − 0.823629I
a = 0.412890 + 0.456902I
b = 0.679306 − 1.137690I
6.90977 + 8.77559I 9.73876 − 7.09449I
u = −0.493094 + 1.098780I
a = −0.387144 − 0.128784I
b = 0.098682 − 0.905560I
5.88215 + 2.52726I 13.28929 − 3.43101I
u = −0.493094 − 1.098780I
a = −0.387144 + 0.128784I
b = 0.098682 + 0.905560I
5.88215 − 2.52726I 13.28929 + 3.43101I
u = 0.622591
a = 0.542539
b = 0.127481
0.865875 12.3760
u = 1.45633 + 0.05562I
a = 0.38364 − 1.65172I
b = −0.429494 + 1.051770I
4.42897 + 2.24150I 6.33861 − 3.08717I
u = 1.45633 − 0.05562I
a = 0.38364 + 1.65172I
b = −0.429494 − 1.051770I
4.42897 − 2.24150I 6.33861 + 3.08717I
u = −0.303715 + 0.334799I
a = 0.003671 + 1.353790I
b = −0.729605 − 0.382323I
−1.31044 − 0.99980I −2.51765 + 3.01751I
u = −0.303715 − 0.334799I
a = 0.003671 − 1.353790I
b = −0.729605 + 0.382323I
−1.31044 + 0.99980I −2.51765 − 3.01751I
5