If z and omega are two complex numbers such that

eSaral Updated on:
Question:

If $z$ and $\omega$ are two complex numbers such that $|z \omega|=1$ and $\arg (z)-\arg (\omega)=\frac{\pi}{2}$, then:

  1. (1) $\bar{z} \omega=i$

  2. (2) $z \bar{\omega}=\frac{-1+i}{\sqrt{2}}$

  3. (3) $\bar{z} \omega=-i$

  4. (4) $z \bar{\omega}=\frac{1-i}{\sqrt{2}}$

Correct Option: , 3

Solution:

Given $|z \omega|=1$

and $\arg \left(\frac{z}{\omega}\right)=\frac{\pi}{2}$

 

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