If \( z_{1}=a+\mathrm{ib} \) and \( z_{2}=c+\mathrm{id} \) two complex numbers lying on the circ... VIDEO
If \( z_{1}=a+\mathrm{ib} \) and \( z_{2}=c+\mathrm{id} \) two complex numbers lying on the circle \( x^{2}+y^{2}=1 \) in the Argand diagram and \( \operatorname{Re}\left(z_{1} \bar{z}_{2}\right)=0 \) then the complex numbers \( \omega_{1}=(a+ \) ic \( ) \) and \( \omega_{2}=b+\mathrm{id} \) are such that
(a) Only \( \omega_{1} \) lies on the circle \( x^{2}+y^{2}=1 \)
(b) Only \( \omega_{2} \) lies on the circle \( x^{2}+y^{2}=1 \)
(c) \( \operatorname{Re}\left(\omega_{1} \bar{\omega}_{2}\right)=0 \)
(d) \( \operatorname{Im}\left(\omega_{1} \bar{\omega}_{2}\right)=0 \)
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