![](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 = −0.990309 + 0.197371I
0.77149 − 3.51641I −4.00000 + 4.68932I
u = −0.990309 − 0.197371I
0.77149 + 3.51641I −4.00000 − 4.68932I
u = 0.983886 + 0.233964I
−4.05748 + 7.29975I 0. − 6.02392I
u = 0.983886 − 0.233964I
−4.05748 − 7.29975I 0. + 6.02392I
u = 0.917926
−1.63623 −6.25380
u = −0.855417 + 0.248728I
−8.04962 + 0.09735I −10.00686 + 0.77062I
u = −0.855417 − 0.248728I
−8.04962 − 0.09735I −10.00686 − 0.77062I
u = 0.738976 + 0.315928I
−3.71204 − 7.38704I −6.03668 + 3.97983I
u = 0.738976 − 0.315928I
−3.71204 + 7.38704I −6.03668 − 3.97983I
u = 1.20059
−1.54443 0
u = 0.262184 + 0.729860I
−5.40381 + 11.28260I −8.66884 − 8.74113I
u = 0.262184 − 0.729860I
−5.40381 − 11.28260I −8.66884 + 8.74113I
u = −0.710255 + 0.292534I
1.06112 + 3.49327I −1.18332 − 2.67462I
u = −0.710255 − 0.292534I
1.06112 − 3.49327I −1.18332 + 2.67462I
u = −0.262033 + 0.720142I
−0.59286 − 7.29825I −4.05645 + 7.44817I
u = −0.262033 − 0.720142I
−0.59286 + 7.29825I −4.05645 − 7.44817I
u = −0.224274 + 0.729292I
−10.09160 − 3.88890I −12.88295 + 4.18648I
u = −0.224274 − 0.729292I
−10.09160 + 3.88890I −12.88295 − 4.18648I
u = 0.256468 + 0.700542I
−3.25124 + 3.34292I −7.24196 − 3.75335I
u = 0.256468 − 0.700542I
−3.25124 − 3.34292I −7.24196 + 3.75335I
u = 0.176621 + 0.719075I
−6.50527 − 3.62888I −10.79295 + 1.37881I
u = 0.176621 − 0.719075I
−6.50527 + 3.62888I −10.79295 − 1.37881I
u = 0.224321 + 0.695502I
−3.61835 + 3.40694I −9.07650 − 5.66068I
u = 0.224321 − 0.695502I
−3.61835 − 3.40694I −9.07650 + 5.66068I
u = −0.354761 + 0.564052I
0.22062 − 5.60280I −3.25617 + 7.64930I
u = −0.354761 − 0.564052I
0.22062 + 5.60280I −3.25617 − 7.64930I
u = −1.317080 + 0.220326I
−0.01372 − 5.66365I 0
u = −1.317080 − 0.220326I
−0.01372 + 5.66365I 0
u = 0.610474 + 0.243113I
−1.66667 + 0.22451I −3.98223 − 1.07282I
u = 0.610474 − 0.243113I
−1.66667 − 0.22451I −3.98223 + 1.07282I
5