Let $\alpha$ and $\beta$ be two nonzero complex numbers. For $z \in \mathbb{C}, \bar{z}$ denotes the complex conjugate of $z$. If the lines $\alpha \bar{z}+\bar{\alpha} z=-1$ and $\beta \bar{z}+\bar{\beta} z=1$ are mutually perpendicular then

• A

  $\bar{\alpha} \beta-\alpha \bar{\beta}=0$
• B

  $\alpha \beta-\bar{\alpha} \bar{\beta}=0$
• Correct answer
  C

  $\bar{\alpha} \beta+\alpha \bar{\beta}=0$
• D

  $\alpha \beta+\bar{\alpha} \bar{\beta}=0$

Hence, the correct answer is option: 'C'.