Let $z_1=a+i b$ and $z_2=c+i d$ be complex numbers such that $\left|z_1\right|=\left|z_2\right|=1$ and $\operatorname{Re}\left(z_1 \overline{z_2}\right)=0$. Then the complex numbers $w_1=a+i c$ and $w_2=b+i d$ always satisfy

• Correct answer
  A

  $\left|w_1\right|=\left|w_2\right|$
• B

  $\operatorname{Re}\left(w_1\right)=\operatorname{Im}\left(w_2\right)$
• Correct answer
  C

  $\operatorname{Re}\left(w_1 \overline{w_2}\right)=0$
• Correct answer
  D

  $\operatorname{Re}\left(w_1 w_2\right)=2 \operatorname{Re}\left(w_1\right) \operatorname{Re}\left(w_2\right)$

Hence, the correct answer is options: 'A', 'C', 'D'.