Complex Numbers And Quadratic Equations question 124
Question: If $ {{(\sqrt{8}+i)}^{50}}=3^{49}(a+ib) $ then $ a^{2}+b^{2} $ is [Kerala (Engg.) 2005]
Options:
A) 3
B) 8
C) 9
D) $ \sqrt{8} $
E) 4
Show Answer
Answer:
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 $ .
BETA
