$(-1)/(2i/\{-2\lambda\})=-i\lambda$ - this can't be true?

Question

Maybe I am confused but in the screenshot below, there is a line saying that $$ c_1=(-1)/(2i/\{-2\lambda\})=-i\lambda,\qquad \hat{c_1}=(-1)/(2i/2\lambda)=i\lambda. $$

Isn't that false? Shouldn't it be $$ c_1=(-1)/(2i/\{-2\lambda\})=\lambda/i,\qquad \hat{c_1}=(-1)/(2i/2\lambda)=-\lambda/i? $$

By the way: The formula behind that is $$ c_1=b(\zeta)/(da/d\zeta) $$ evaluated at $\zeta=\frac{i\lambda}{2}$.

Answer 1

Since $\frac1i=-i$, there is no contradiction.