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If ${(1 + i)}^{100} = 2^{49} (x + i y)$ ,then $x^{2} + y^{2} =$

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Detailed Solution

${(1 + i)}^{100} = 2^{49} (x + i y)$

${[{(1 + i)}^{2}]}^{50} = 2^{49} (x + i y)$

${(2 i)}^{50} = 2^{49} (x + i y)$

$2^{50} . i^{50} = 2^{49} (x + i y)$

$2. i^{4 \times 12 + 2} = x + i y$

$(- 2) = x + i y$

$x = - 2, y = 0, x^{2} y^{2} = 4$

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