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For two unimodular complex numbers $z_{1} a n d z_{2,} {[\begin{matrix} \bar{z_{1}} & - z_{2} \\ \bar{z_{2}} & z_{1} \end{matrix}]}^{- 1} {[\begin{matrix} z_{1} & z_{2} \\ - \bar{z_{2}} & \bar{z_{1}} \end{matrix}]}^{- 1}$ is equal to

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z1z2z1¯z2¯

1001

1/2001/2

none of these

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detailed solution

Correct option is C

Z1=Z2=1z1¯−z2z2¯z1−1z1z2−z2¯z1¯−1=z1z2−z2¯z1¯z1¯−z2z2¯z1−1=z1z1¯+z2z2¯00z2z2¯+z1z¯1−1=z12+z2200z12+z22−1 ∴ZZ¯=|Z|2=2002−1=1/2001/2

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For two unimodular complex numbers z1 and z2,z1¯−z2z2¯z1−1z1z2−z2¯z1¯−1 is equal to

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For two unimodular complex numbers $z_{1} a n d z_{2,} {[\begin{matrix} \bar{z_{1}} & - z_{2} \\ \bar{z_{2}} & z_{1} \end{matrix}]}^{- 1} {[\begin{matrix} z_{1} & z_{2} \\ - \bar{z_{2}} & \bar{z_{1}} \end{matrix}]}^{- 1}$ is equal to