If z_1 and z_2 are two unimodular complex num | vedclass

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(A) Given that $z_1$ and $z_2$ are unimodular,we have $|z_1| = 1$ and $|z_2| = 1.$Since $|z|^2 = z \bar{z} = 1$,we have $\bar{z}_1 = \frac{1}{z_1}$ an

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$6$

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(A) Given that $z_1$ and $z_2$ are unimodular,we have $|z_1| = 1$ and $|z_2| = 1.$Since $|z|^2 = z \bar{z} = 1$,we have $\bar{z}_1 = \frac{1}{z_1}$ and $\bar{z}_2 = \frac{1}{z_2}.$Given $z_1^2 + z_2^2 = 5.$We need to evaluate $E = (z_1 - \bar{z}_1)^2 + (z_2 - \bar{z}_2)^2.$Expanding the terms: $E = (z_1^2 + \bar{z}_1^2 - 2z_1\bar{z}_1) + (z_2^2 + \bar{z}_2^2 - 2z_2\bar{z}_2).$Since $z_1\bar{z}_1 = |z_1|^2 = 1$ and $z_2\bar{z}_2 = |z_2|^2 = 1$,we have:$E = (z_1^2 + z_2^2) + (\bar{z}_1^2 + \bar{z}_2^2) - 2(1) - 2(1).$Since $z_1^2 + z_2^2 = 5$,taking the conjugate gives $\bar{z}_1^2 + \bar{z}_2^2 = \bar{5} = 5.$Substituting these values: $E = 5 + 5 - 4 = 6.$

If $z_1$ and $z_2$ are two unimodular complex numbers that satisfy $z_1^2 + z_2^2 = 5,$ then $(z_1 - \bar{z}_1)^2 + (z_2 - \bar{z}_2)^2$ is equal to -

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