![](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 = −0.543476 + 0.874447I
1.82954 − 5.19769I 6.15709 + 8.44602I
u = −0.543476 − 0.874447I
1.82954 + 5.19769I 6.15709 − 8.44602I
u = 0.619141 + 0.725788I
0.22503 + 2.28348I 5.46937 − 4.01207I
u = 0.619141 − 0.725788I
0.22503 − 2.28348I 5.46937 + 4.01207I
u = −0.370456 + 0.868836I
−5.30643 − 0.72543I −2.57924 + 3.52341I
u = −0.370456 − 0.868836I
−5.30643 + 0.72543I −2.57924 − 3.52341I
u = 0.530210 + 0.918792I
−3.36171 + 8.57781I 0.89148 − 8.59823I
u = 0.530210 − 0.918792I
−3.36171 − 8.57781I 0.89148 + 8.59823I
u = 0.499339 + 0.766815I
0.29678 + 1.94361I 2.76791 − 3.40470I
u = 0.499339 − 0.766815I
0.29678 − 1.94361I 2.76791 + 3.40470I
u = −0.086945 + 0.906060I
−6.77422 − 3.97739I −5.33902 + 4.43736I
u = −0.086945 − 0.906060I
−6.77422 + 3.97739I −5.33902 − 4.43736I
u = −0.633646 + 0.581658I
2.77033 + 0.77167I 9.84736 − 1.25670I
u = −0.633646 − 0.581658I
2.77033 − 0.77167I 9.84736 + 1.25670I
u = 0.669966 + 0.509743I
−2.05362 − 4.10467I 4.51219 + 2.60017I
u = 0.669966 − 0.509743I
−2.05362 + 4.10467I 4.51219 − 2.60017I
u = 0.084712 + 0.809947I
−1.49083 + 1.38540I −1.60809 − 5.67489I
u = 0.084712 − 0.809947I
−1.49083 − 1.38540I −1.60809 + 5.67489I
u = 0.854791 + 0.915240I
1.86062 + 3.17602I 1.83589 − 2.52504I
u = 0.854791 − 0.915240I
1.86062 − 3.17602I 1.83589 + 2.52504I
u = −0.914545 + 0.890982I
6.06012 + 4.90822I 4.65952 − 2.34927I
u = −0.914545 − 0.890982I
6.06012 − 4.90822I 4.65952 + 2.34927I
u = 0.910016 + 0.903339I
11.15980 − 1.02259I 9.09851 + 1.19971I
u = 0.910016 − 0.903339I
11.15980 + 1.02259I 9.09851 − 1.19971I
u = −0.898949 + 0.919422I
9.01203 − 3.04738I 6.19226 + 3.43104I
u = −0.898949 − 0.919422I
9.01203 + 3.04738I 6.19226 − 3.43104I
u = −0.887948 + 0.940225I
8.94377 − 3.54704I 6.02010 + 1.31518I
u = −0.887948 − 0.940225I
8.94377 + 3.54704I 6.02010 − 1.31518I
u = 0.883193 + 0.957672I
10.98400 + 7.63582I 8.68172 − 5.95948I
u = 0.883193 − 0.957672I
10.98400 − 7.63582I 8.68172 + 5.95948I
5