a circle when $\left|z_1-z_2\right|<\lambda$

a parabola when $\left|z_1+z_2\right|=\lambda$

an ellipse when $\left|z_1-z_2\right|<\lambda$

a straight line when $\left|z_1\right|=\left|z_2\right|=\lambda$

$\frac{1+2 e^{\frac{2 k \pi i}{5}}}{1-2 e^{\frac{2 k \pi i}{5}}}, k=1,2,3,4,5$

$\frac{1-2 e^{\frac{2 k \pi i}{5}}}{1+2 e^{\frac{2 k \pi i}{5}}}, k=0,1,2,3,4$

$1,2 \omega, 3 \omega^2, 2 \omega+3 \omega^2, 5 \omega^2+7$

$\frac{3+2 e^{\frac{2(k+1) \pi i}{5}}}{3-2 e^{\frac{2(k+1) \pi i}{5}}}, k=0,1,2,3,4$

5

7

12

-19

5

1

$\frac{1}{2}$

2