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Given equation is

$$({\sqrt{8}+i})^{50} = 3^{49}(a+ib)$$

take the conjugate on both sides

$$({\sqrt{8}-i})^{50} = 3^{49}(a-ib)$$

After multiplying both equations we will get,

$${9}^{50} = 3^{98}(a^2 + b^2)$$

$$ (a^2 + b^2) = 9$$
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