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If \( z_{1}=a+i b \) and \( z_{2}=c+i d \) are two complex numbers such that \( \left|z_{1}\right|=\left|z_{2}\right|=1 \) and \( \operatorname{Re}\left(z_{1} \bar{z}_{2}\right)=0 \), then the pair of complex numbers, \( w_{1}=a+i c \) and \( w_{2}=b+i d \) satisfy
(a) \( \left|w_{1}\right|=1 \)
(b) \( \left|w_{2}\right|=1 \)
(c) \( \left|w_{1} \quad \bar{w}_{2}\right|=1 \)
(d) \( \operatorname{Re}\left(\bar{w}_{1} w_{2}\right)=0 \)
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