![](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 = −0.277924 + 0.951909I
−3.90188 − 2.73159I −14.1982 + 4.9259I
u = −0.277924 − 0.951909I
−3.90188 + 2.73159I −14.1982 − 4.9259I
u = −0.171363 + 0.973104I
6.85402 + 1.62529I −8.25292 + 0.49765I
u = −0.171363 − 0.973104I
6.85402 − 1.62529I −8.25292 − 0.49765I
u = 0.322382 + 0.965498I
−1.09525 + 5.77920I −7.86814 − 8.38864I
u = 0.322382 − 0.965498I
−1.09525 − 5.77920I −7.86814 + 8.38864I
u = 0.218790 + 0.942416I
−1.70142 − 0.27515I −9.76443 + 0.48327I
u = 0.218790 − 0.942416I
−1.70142 + 0.27515I −9.76443 − 0.48327I
u = −0.349470 + 0.985821I
7.87866 − 7.40221I −6.00523 + 6.67601I
u = −0.349470 − 0.985821I
7.87866 + 7.40221I −6.00523 − 6.67601I
u = 0.605298 + 0.622434I
12.21750 + 2.21577I 0.00606 − 3.15863I
u = 0.605298 − 0.622434I
12.21750 − 2.21577I 0.00606 + 3.15863I
u = 0.724879 + 0.902558I
11.90850 + 2.74938I −2.70691 − 3.06690I
u = 0.724879 − 0.902558I
11.90850 − 2.74938I −2.70691 + 3.06690I
u = −0.806200 + 0.845885I
4.50177 − 2.35046I −3.49635 + 4.76108I
u = −0.806200 − 0.845885I
4.50177 + 2.35046I −3.49635 − 4.76108I
u = 0.834116 + 0.820628I
3.12542 − 0.75919I −6.95792 + 1.59263I
u = 0.834116 − 0.820628I
3.12542 + 0.75919I −6.95792 − 1.59263I
u = −0.858422 + 0.817028I
6.46803 + 3.80376I −1.40821 − 3.43849I
u = −0.858422 − 0.817028I
6.46803 − 3.80376I −1.40821 + 3.43849I
u = 0.874607 + 0.815183I
15.8059 − 5.4998I −0.14982 + 1.94040I
u = 0.874607 − 0.815183I
15.8059 + 5.4998I −0.14982 − 1.94040I
u = −0.782409 + 0.935028I
4.22457 − 3.61643I −4.15250 + 0.77790I
u = −0.782409 − 0.935028I
4.22457 + 3.61643I −4.15250 − 0.77790I
u = −0.470068 + 0.618631I
3.05318 − 1.77992I 0.16951 + 4.97625I
u = −0.470068 − 0.618631I
3.05318 + 1.77992I 0.16951 − 4.97625I
u = 0.836155 + 0.902083I
9.93224 + 3.11134I 1.49937 − 2.73102I
u = 0.836155 − 0.902083I
9.93224 − 3.11134I 1.49937 + 2.73102I
u = 0.791521 + 0.959516I
2.69617 + 6.83503I −8.00000 − 6.45647I
u = 0.791521 − 0.959516I
2.69617 − 6.83503I −8.00000 + 6.45647I
5