Let x and y be real number such that$50\left( \frac{2x}{1 + 3i} - \frac{y}{1 - 2i} \right) = 31 + 17

Question

Let x and y be real number such that$50\left( \frac{2x}{1 + 3i} - \frac{y}{1 - 2i} \right) = 31 + 17i,\ \ i = \sqrt{- 1}$.Then the value of $10(x - 3y)$ is :

Accepted Answer

Sol. [Key Concept: Rationalize each fraction, then equate real and imaginary parts to solve for $x$ and $y$.]$$\ 50\left( \frac{2x(1 - 3i)}{10} - \frac{y(1 + 2i)}{5} ight) = 31 + 17i $$$$10x - (30x)i - 10y - 20yi = 31 + 17i $$$$\left. \ \begin{matrix} 10(x - y) = 31 \ - 30x - 20y = 17 \end{matrix} ight\} $$$$30x - 30y = 93 $$$$- 10(3x + 2y) = 17 $$$$x = 0.9,y = - 2.2 $$$$10(x - 3y) = 75 $$

Question

Options

Solution

More Complex Numbers Questions