![](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 = 0.946141 + 0.011490I
−13.5904 − 5.0425I −10.78024 + 2.84693I
u = 0.946141 − 0.011490I
−13.5904 + 5.0425I −10.78024 − 2.84693I
u = 0.416424 + 0.993762I
0.95586 + 5.59232I −9.07345 − 8.52361I
u = 0.416424 − 0.993762I
0.95586 − 5.59232I −9.07345 + 8.52361I
u = −0.327821 + 1.035380I
−3.20510 − 2.90050I −16.7585 + 6.2360I
u = −0.327821 − 1.035380I
−3.20510 + 2.90050I −16.7585 − 6.2360I
u = 0.153534 + 0.829883I
−0.664834 + 0.970955I −10.56839 − 6.31245I
u = 0.153534 − 0.829883I
−0.664834 − 0.970955I −10.56839 + 6.31245I
u = −0.373530 + 0.720587I
3.67591 − 1.72367I −3.04572 + 4.67737I
u = −0.373530 − 0.720587I
3.67591 + 1.72367I −3.04572 − 4.67737I
u = −0.768463 + 0.066318I
−2.56255 + 4.06172I −9.74928 − 3.64554I
u = −0.768463 − 0.066318I
−2.56255 − 4.06172I −9.74928 + 3.64554I
u = −0.454887 + 1.179480I
−5.83119 − 8.50268I −12.8572 + 7.0300I
u = −0.454887 − 1.179480I
−5.83119 + 8.50268I −12.8572 − 7.0300I
u = 0.425814 + 1.198730I
−9.89307 + 4.30260I −17.3404 − 3.7895I
u = 0.425814 − 1.198730I
−9.89307 − 4.30260I −17.3404 + 3.7895I
u = 0.487685 + 1.287980I
−17.5204 + 10.1457I −13.8263 − 5.6856I
u = 0.487685 − 1.287980I
−17.5204 − 10.1457I −13.8263 + 5.6856I
u = −0.481775 + 1.292500I
17.8662 − 5.0843I −17.1007 + 2.8764I
u = −0.481775 − 1.292500I
17.8662 + 5.0843I −17.1007 − 2.8764I
u = 0.476877 + 0.292674I
2.80571 − 1.90068I −4.89982 + 3.73749I
u = 0.476877 − 0.292674I
2.80571 + 1.90068I −4.89982 − 3.73749I
5