![](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 = 0.599044 + 0.826443I
2.20023 + 0.03981I 1.90801 + 0.I
u = 0.599044 − 0.826443I
2.20023 − 0.03981I 1.90801 + 0.I
u = 0.516168 + 0.894544I
−2.24111 + 4.14051I −5.37917 − 5.76586I
u = 0.516168 − 0.894544I
−2.24111 − 4.14051I −5.37917 + 5.76586I
u = −0.575209 + 0.860059I
3.33392 − 4.67344I 3.60111 + 7.51773I
u = −0.575209 − 0.860059I
3.33392 + 4.67344I 3.60111 − 7.51773I
u = −0.417668 + 0.858179I
−3.47104 − 4.65742I −7.34835 + 7.77657I
u = −0.417668 − 0.858179I
−3.47104 + 4.65742I −7.34835 − 7.77657I
u = −0.548997 + 0.901918I
2.20323 − 6.68220I 0. + 7.34850I
u = −0.548997 − 0.901918I
2.20323 + 6.68220I 0. − 7.34850I
u = 0.662569 + 0.668001I
2.71906 + 4.65572I 3.37494 − 5.91636I
u = 0.662569 − 0.668001I
2.71906 − 4.65572I 3.37494 + 5.91636I
u = 0.545262 + 0.916750I
−0.02627 + 11.64450I 0. − 11.11786I
u = 0.545262 − 0.916750I
−0.02627 − 11.64450I 0. + 11.11786I
u = −0.658358 + 0.624266I
4.09825 + 0.06503I 6.21402 − 0.17680I
u = −0.658358 − 0.624266I
4.09825 − 0.06503I 6.21402 + 0.17680I
u = −0.331173 + 0.844557I
−2.52809 + 2.55717I −6.16177 + 0.11362I
u = −0.331173 − 0.844557I
−2.52809 − 2.55717I −6.16177 − 0.11362I
u = −0.111108 + 0.897806I
−3.65266 − 7.15580I −8.25035 + 7.79317I
u = −0.111108 − 0.897806I
−3.65266 + 7.15580I −8.25035 − 7.79317I
u = −0.056026 + 0.881651I
−5.32447 + 0.22926I −11.87724 + 0.46623I
u = −0.056026 − 0.881651I
−5.32447 − 0.22926I −11.87724 − 0.46623I
u = 0.112571 + 0.866237I
−1.39262 + 2.45864I −5.10441 − 4.27623I
u = 0.112571 − 0.866237I
−1.39262 − 2.45864I −5.10441 + 4.27623I
u = −0.669205 + 0.554761I
3.32166 + 2.13457I 5.05558 − 0.87891I
u = −0.669205 − 0.554761I
3.32166 − 2.13457I 5.05558 + 0.87891I
u = 0.683206 + 0.533126I
1.20996 − 7.07293I 1.66097 + 5.05839I
u = 0.683206 − 0.533126I
1.20996 + 7.07293I 1.66097 − 5.05839I
u = 0.397569 + 0.766288I
−0.23774 + 1.55359I −1.92023 − 4.37944I
u = 0.397569 − 0.766288I
−0.23774 − 1.55359I −1.92023 + 4.37944I
5