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JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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If z0=1−iz,{z_0} = \frac{{1 - i}}{z}, then the value of the product (1+z0)(1+z02)(1+z022)(1+z022)…(1+z022)\left( {1 + {z_0}} \right)\left( {1 + z_0^2} \right)\left( {1 + z_0^{{2^2}}} \right)\left( {1 + z_0^{{2^2}}} \right) \ldots \left( {1 + z_0^{{2^2}}} \right) must be
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Correct option: B
(1−i)(1−122n),  if  n>1\left( {1 - i} \right)\left( {1 - \frac{1}{{{2^{{2^n}}}}}} \right),\;\mathrm{if}\;n > 1
Option B is correct. The product simplifies to a closed form expression involving z_0 and its powers, ultimately leading to the given result.

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