![](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 = −0.803360 + 0.638492I
2.78379 + 9.20045I −4.00000 − 5.04305I
u = −0.803360 − 0.638492I
2.78379 − 9.20045I −4.00000 + 5.04305I
u = 0.800124 + 0.647068I
7.09459 − 4.72698I 0. + 2.48714I
u = 0.800124 − 0.647068I
7.09459 + 4.72698I 0. − 2.48714I
u = −0.794421 + 0.657199I
3.54889 + 0.19967I 0
u = −0.794421 − 0.657199I
3.54889 − 0.19967I 0
u = −0.729773 + 0.636528I
0.83498 + 2.07700I −1.30731 − 4.65040I
u = −0.729773 − 0.636528I
0.83498 − 2.07700I −1.30731 + 4.65040I
u = 0.701441 + 0.764368I
0.332471 − 0.137935I −4.00000 + 0.I
u = 0.701441 − 0.764368I
0.332471 + 0.137935I −4.00000 + 0.I
u = 0.751806 + 0.599939I
−4.30064 − 4.22428I −7.11593 + 3.82963I
u = 0.751806 − 0.599939I
−4.30064 + 4.22428I −7.11593 − 3.82963I
u = 0.022057 + 1.053290I
−4.58704 + 1.51218I −9.45944 − 4.55261I
u = 0.022057 − 1.053290I
−4.58704 − 1.51218I −9.45944 + 4.55261I
u = 0.096493 + 1.057100I
−2.57943 − 0.08281I −8.50549 + 0.I
u = 0.096493 − 1.057100I
−2.57943 + 0.08281I −8.50549 + 0.I
u = −0.669102 + 0.844952I
3.28932 − 2.58275I 0
u = −0.669102 − 0.844952I
3.28932 + 2.58275I 0
u = 0.529127 + 0.939240I
−0.06741 + 5.98627I 0
u = 0.529127 − 0.939240I
−0.06741 − 5.98627I 0
u = 0.647786 + 0.655651I
0.241433 + 0.748431I −4.13794 − 3.90803I
u = 0.647786 − 0.655651I
0.241433 − 0.748431I −4.13794 + 3.90803I
u = −0.092376 + 1.074670I
0.91363 − 4.29574I 0
u = −0.092376 − 1.074670I
0.91363 + 4.29574I 0
u = −0.028914 + 1.086230I
−9.95694 − 3.35433I −14.2561 + 0.I
u = −0.028914 − 1.086230I
−9.95694 + 3.35433I −14.2561 + 0.I
u = 0.087961 + 1.086010I
−3.41796 + 8.65689I 0
u = 0.087961 − 1.086010I
−3.41796 − 8.65689I 0
u = −0.558836 + 0.972282I
3.64416 − 1.88415I 0
u = −0.558836 − 0.972282I
3.64416 + 1.88415I 0
5