![](data:image/png;base64,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)
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.752589 + 0.686692I
a = −1.19861 − 1.00203I
b = 1.75066 − 0.28301I
0.134724 − 0.617454I 7.60333 + 0.92062I
u = 0.752589 − 0.686692I
a = −1.19861 + 1.00203I
b = 1.75066 + 0.28301I
0.134724 + 0.617454I 7.60333 − 0.92062I
u = 1.021920 + 0.291673I
a = −0.675586 − 0.356154I
b = 0.0136506 − 0.1110620I
0.134724 + 0.617454I 7.60333 − 0.92062I
u = 1.021920 − 0.291673I
a = −0.675586 + 0.356154I
b = 0.0136506 + 0.1110620I
0.134724 − 0.617454I 7.60333 + 0.92062I
u = −0.842250 + 0.401014I
a = −0.301397 + 0.041356I
b = −0.014640 − 1.010940I
0.11473 − 4.15162I 6.01126 + 6.89813I
u = −0.842250 − 0.401014I
a = −0.301397 − 0.041356I
b = −0.014640 + 1.010940I
0.11473 + 4.15162I 6.01126 − 6.89813I
u = −0.752492 + 0.788189I
a = −1.69455 + 1.94272I
b = 2.70085 − 0.03238I
−2.50569 + 4.90020I 3.66047 − 4.25570I
u = −0.752492 − 0.788189I
a = −1.69455 − 1.94272I
b = 2.70085 + 0.03238I
−2.50569 − 4.90020I 3.66047 + 4.25570I
u = 0.951867 + 0.554822I
a = −1.110860 + 0.329191I
b = 0.36805 − 1.46263I
−0.330999 4.51777 + 0.I
u = 0.951867 − 0.554822I
a = −1.110860 − 0.329191I
b = 0.36805 + 1.46263I
−0.330999 4.51777 + 0.I
11