![](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 = −0.007642 + 0.966456I
−11.28980 − 3.26800I −8.22072 + 2.51230I
u = −0.007642 − 0.966456I
−11.28980 + 3.26800I −8.22072 − 2.51230I
u = −0.455339 + 0.953830I
−8.76382 − 2.08770I −4.31619 + 3.32105I
u = −0.455339 − 0.953830I
−8.76382 + 2.08770I −4.31619 − 3.32105I
u = −0.424765 + 0.837410I
−1.06965 − 2.01513I −4.12618 + 3.84559I
u = −0.424765 − 0.837410I
−1.06965 + 2.01513I −4.12618 − 3.84559I
u = 0.468864 + 0.955282I
−8.59119 + 8.60337I −3.84612 − 8.10725I
u = 0.468864 − 0.955282I
−8.59119 − 8.60337I −3.84612 + 8.10725I
u = 0.547826 + 0.720762I
2.87673 + 2.07761I 8.03109 − 4.87367I
u = 0.547826 − 0.720762I
2.87673 − 2.07761I 8.03109 + 4.87367I
u = −0.054899 + 0.842893I
−2.87673 − 2.07761I −8.03109 + 4.87367I
u = −0.054899 − 0.842893I
−2.87673 + 2.07761I −8.03109 − 4.87367I
u = 0.675982 + 0.376953I
−6.76036 − 4.39632I 0.35650 + 2.56566I
u = 0.675982 − 0.376953I
−6.76036 + 4.39632I 0.35650 − 2.56566I
u = 0.570879 + 0.520043I
1.06965 − 2.01513I 4.12618 + 3.84559I
u = 0.570879 − 0.520043I
1.06965 + 2.01513I 4.12618 − 3.84559I
u = 0.897344 + 0.861664I
0.784836I 0. − 2.11264I
u = 0.897344 − 0.861664I
− 0.784836I 0. + 2.11264I
u = −0.666629 + 0.352689I
−6.87304 − 2.02249I 0.14883 + 2.38441I
u = −0.666629 − 0.352689I
−6.87304 + 2.02249I 0.14883 − 2.38441I
u = −0.903766 + 0.864696I
0.34673 + 5.67431I 0.59636 − 2.67543I
u = −0.903766 − 0.864696I
0.34673 − 5.67431I 0.59636 + 2.67543I
u = 0.873303 + 0.899277I
6.87304 + 2.02249I 0. − 2.38441I
u = 0.873303 − 0.899277I
6.87304 − 2.02249I 0. + 2.38441I
u = −0.893753 + 0.895948I
8.76382 + 2.08770I 4.31619 − 3.32105I
u = −0.893753 − 0.895948I
8.76382 − 2.08770I 4.31619 + 3.32105I
u = 0.858890 + 0.934946I
6.76036 + 4.39632I 0. − 2.56566I
u = 0.858890 − 0.934946I
6.76036 − 4.39632I 0. + 2.56566I
u = −0.350675 + 0.633429I
−0.162533 − 1.134740I −3.04903 + 5.46701I
u = −0.350675 − 0.633429I
−0.162533 + 1.134740I −3.04903 − 5.46701I
5