What is the value of \sqrt{12+5i}+\sqrt{12-5i}, where i=\sqrt{-1}?
- A. 24
- B. 25
- C. 5\sqrt{2} ✓
- D. 5(\sqrt{2}-1)
Correct Answer: C. 5\sqrt{2}
Explanation
Let x = \sqrt{12+5i} + \sqrt{12-5i}. Squaring both sides gives x^2 = (12+5i) + (12-5i) + 2\sqrt{144 - 25i^2}. Since i^2=-1, x^2 = 24 + 2\sqrt{169} = 24 + 2(13) = 50. Thus, x = \sqrt{50} = 5\sqrt{2}.
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