AP EAMCET · Maths · Complex Number
If \((x+i y)^{\frac{1}{3}}=5+3 i\), then \(3 x+5 y=\)
- A \(480\)
- B \(152\)
- C \(990\)
- D \(960\)
Answer & Solution
Correct Answer
(D) \(960\)
Step-by-step Solution
Detailed explanation
\((x+iy) = (5+3i)^3\) \((x+iy) = 5^3 + 3(5^2)(3i) + 3(5)(3i)^2 + (3i)^3\) \((x+iy) = 125 + 225i + 15(-9) + (-27i)\) \((x+iy) = 125 + 225i - 135 - 27i\) \((x+iy) = -10 + 198i\) \(x = -10, y = 198\) \(3x+5y = 3(-10) + 5(198)\) \(3x+5y = -30 + 990\) \(3x+5y = 960\)
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