Solve (lambda-1/2)^2+(mu+1)^2=1

$$( \lambda - \frac { 1 } { 2 } ) ^ { 2 } + ( \mu + 1 ) ^ { 2 } = 1$$

Solve for λ (complex solution)

$$\lambda =-i\sqrt{\mu }\sqrt{\mu +2}+\frac{1}{2}$$

$$\lambda =i\sqrt{\mu }\sqrt{\mu +2}+\frac{1}{2}$$

Solve for μ (complex solution)

$$\mu =-\frac{\sqrt{3+4\lambda -4\lambda ^{2}}}{2}-1$$

$$\mu =\frac{\sqrt{3+4\lambda -4\lambda ^{2}}}{2}-1$$

Solve for λ

$$\lambda =-\sqrt{-\mu ^{2}-2\mu }+\frac{1}{2}$$

$$\lambda =\sqrt{-\mu ^{2}-2\mu }+\frac{1}{2}\text{, }\mu \geq -2\text{ and }\mu \leq 0$$

Solve for μ

$$\mu =-\frac{\sqrt{3+4\lambda -4\lambda ^{2}}}{2}-1$$

$$\mu =\frac{\sqrt{3+4\lambda -4\lambda ^{2}}}{2}-1\text{, }\lambda \geq -\frac{1}{2}\text{ and }\lambda \leq \frac{3}{2}$$