JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(x\) and \(y\) be real numbers such that \(50\left(\dfrac{2x}{1+3i} - \dfrac{y}{1-2i}\right) = 31 + 17i\), \(i = \sqrt{-1}\). Then the value of \(10(x - 3y)\) is :
- A \(20\)
- B \(31\)
- C \(35\)
- D \(75\)
Answer & Solution
Correct Answer
(D) \(75\)
Step-by-step Solution
Detailed explanation
Given the equation: \(50\left(\dfrac{2x}{1+3i} - \dfrac{y}{1-2i}\right) = 31 + 17i\) Rationalizing the denominators inside the parentheses: \(\dfrac{2x}{1+3i} = \dfrac{2x(1-3i)}{(1+3i)(1-3i)} = \dfrac{2x(1-3i)}{1^2 + 3^2} = \dfrac{2x(1-3i)}{10} = \dfrac{x(1-3i)}{5}\)…
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