A) \[\overline{z}\,\text{w}=i\]
B) \[\overline{z}\,\text{w}=-i\]
C) \[\,z\,\overline{\text{w}}=\frac{1-i}{\sqrt{2}}\]
D) \[\,z\,\overline{\text{w}}=\frac{-1+i}{\sqrt{2}}\]
Correct Answer: B
Solution :
\[|z|.|\text{w}|=1\,\,\,\,\,\,\,\,\,z=r{{e}^{i(\theta +\pi /2)}}\]and\[\text{w}\,\text{=}\frac{1}{r}{{e}^{i\theta }}\] \[\overline{z.}\text{w}\,\text{=}{{e}^{-i\theta +\pi /2}}.{{e}^{i\theta }}={{e}^{-i}}^{(\pi /2)}=-i\] \[z.\overline{\text{w}}\,\text{=}{{e}^{i(\theta +\pi /2)}}.{{e}^{-i\theta }}={{e}^{i}}^{(\pi /2)}=i\]
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