A) 3
B) 8
C) 9
D) \[\sqrt{8}\]
E) 4
Correct Answer: C
Solution :
\[{{(\sqrt{8}+i)}^{50}}={{3}^{49}}(a+ib)\] Taking modulus and squaring on both sides, we get \[{{(8+1)}^{50}}={{3}^{98}}({{a}^{2}}+{{b}^{2}})\] \[{{9}^{50}}={{3}^{98}}({{a}^{2}}+{{b}^{2}})\] \[{{3}^{100}}={{3}^{98}}({{a}^{2}}+{{b}^{2}})\] Þ \[({{a}^{2}}+{{b}^{2}})=9\].
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