![](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 = −0.998941 + 0.045978I
5.28620 − 0.93871I 15.9673 + 0.9512I
u = −0.998941 − 0.045978I
5.28620 + 0.93871I 15.9673 − 0.9512I
u = −0.728323 + 0.685940I
−3.57521 − 0.97987I 0.260565 + 0.640305I
u = −0.728323 − 0.685940I
−3.57521 + 0.97987I 0.260565 − 0.640305I
u = 1.002230 + 0.089379I
3.67626 + 5.72177I 12.7013 − 6.5868I
u = 1.002230 − 0.089379I
3.67626 − 5.72177I 12.7013 + 6.5868I
u = −0.665641 + 0.720471I
−1.78289 + 5.70739I 3.97022 − 5.89201I
u = −0.665641 − 0.720471I
−1.78289 − 5.70739I 3.97022 + 5.89201I
u = 0.530837 + 0.816404I
6.92563 − 8.79045I 7.25155 + 4.85962I
u = 0.530837 − 0.816404I
6.92563 + 8.79045I 7.25155 − 4.85962I
u = −0.522819 + 0.813333I
8.75278 + 3.37930I 9.83163 − 0.35758I
u = −0.522819 − 0.813333I
8.75278 − 3.37930I 9.83163 + 0.35758I
u = 0.521713 + 0.791233I
3.07937 − 1.57482I 4.02266 + 0.18175I
u = 0.521713 − 0.791233I
3.07937 + 1.57482I 4.02266 − 0.18175I
u = −0.833280 + 0.443412I
0.09032 − 4.10436I 9.88532 + 7.11286I
u = −0.833280 − 0.443412I
0.09032 + 4.10436I 9.88532 − 7.11286I
u = 0.650819 + 0.682385I
0.204162 − 1.159700I 7.88295 + 1.51609I
u = 0.650819 − 0.682385I
0.204162 + 1.159700I 7.88295 − 1.51609I
u = 0.492028 + 0.801217I
7.16166 + 5.41348I 7.59584 − 4.65169I
u = 0.492028 − 0.801217I
7.16166 − 5.41348I 7.59584 + 4.65169I
u = −0.850769 + 0.649712I
−2.04278 − 2.52764I 4.28217 + 3.73621I
u = −0.850769 − 0.649712I
−2.04278 + 2.52764I 4.28217 − 3.73621I
u = 0.823932 + 0.690742I
−4.74803 − 0.75860I −0.678268 + 1.202668I
u = 0.823932 − 0.690742I
−4.74803 + 0.75860I −0.678268 − 1.202668I
u = 0.874578 + 0.686205I
−4.59465 + 6.05228I 0. − 7.84880I
u = 0.874578 − 0.686205I
−4.59465 − 6.05228I 0. + 7.84880I
u = 0.982865 + 0.602859I
2.10133 + 4.69499I 11.88053 − 6.10182I
u = 0.982865 − 0.602859I
2.10133 − 4.69499I 11.88053 + 6.10182I
u = −0.946937 + 0.662515I
−2.91580 − 4.23415I 0. + 5.26094I
u = −0.946937 − 0.662515I
−2.91580 + 4.23415I 0. − 5.26094I
5