![](data:image/png;base64,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)
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.090290I
a = −0.961088 + 0.180402I
b = −0.664122 − 0.999638I
−5.13962 −1.84340
u = − 1.090290I
a = −0.961088 − 0.180402I
b = −0.664122 + 0.999638I
−5.13962 −1.84340
u = 0.258427 + 1.166580I
a = −0.565702 + 1.110660I
b = −0.139231 − 0.937062I
−0.44142 + 5.36486I 3.50284 − 6.38935I
u = 0.258427 − 1.166580I
a = −0.565702 − 1.110660I
b = −0.139231 + 0.937062I
−0.44142 − 5.36486I 3.50284 + 6.38935I
u = −0.258427 + 1.166580I
a = −0.870065 − 0.439798I
b = −0.83736 + 1.51086I
−0.44142 − 5.36486I 3.50284 + 6.38935I
u = −0.258427 − 1.166580I
a = −0.870065 + 0.439798I
b = −0.83736 − 1.51086I
−0.44142 + 5.36486I 3.50284 − 6.38935I
u = 0.892618 + 0.961745I
a = 0.611276 − 0.635790I
b = 0.197106 + 0.382187I
0.89291 − 1.78628I 1.46883 + 8.62602I
u = 0.892618 − 0.961745I
a = 0.611276 + 0.635790I
b = 0.197106 − 0.382187I
0.89291 + 1.78628I 1.46883 − 8.62602I
u = −0.892618 + 0.961745I
a = −0.259050 + 0.347570I
b = 0.227991 + 0.862739I
0.89291 + 1.78628I 1.46883 − 8.62602I
u = −0.892618 − 0.961745I
a = −0.259050 − 0.347570I
b = 0.227991 − 0.862739I
0.89291 − 1.78628I 1.46883 + 8.62602I
16