For Z1=61+i3 1−i ;Z2=63+i1−i ;Z3=63−i1+i which of the following holds good ?

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For Z_{ { 1 } }= [ 6 ]{ { 1-i }{ 1+i { 3 } } } ;Z_{ { 2 }

Question

For $Z_{1} = 6 \frac{1 - i}{1 + i 3}; Z_{2} = 6 \frac{1 - i}{3 + i}; Z_{3} = 6 \frac{1 + i}{3 - i}$ which of the following holds good ?

\sum ∣ Z_{1} ∣^{2} = \frac{3}{2}

∣ Z_{1} ∣^{4} + ∣ Z_{2} ∣^{4} = ∣ Z_{3} ∣^{- 8}

\sum ∣ Z_{1} ∣^{3} + ∣ Z_{2} ∣^{3} = ∣ Z_{3} ∣^{- 6}

∣ Z_{1} ∣^{4} + ∣ Z_{2} ∣^{4} = ∣ Z_{3} ∣^{8}

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For

Z_{1} = 6 \frac{1 - i}{1 + i 3}; Z_{2} = 6 \frac{1 - i}{3 + i}; Z_{3} = 6 \frac{1 + i}{3 - i}

which of the following holds good ?

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Question Text

For

Z_{1} = 6 \frac{1 - i}{1 + i 3}; Z_{2} = 6 \frac{1 - i}{3 + i}; Z_{3} = 6 \frac{1 + i}{3 - i}

which of the following holds good ?