Let x and y be real numbers such that 50 ( 2x 1+3i - y 1-2i ) = 31 + 17i , i = -1 . Then the value of 10(x - 3y) is :

Step-by-step solution

Given the equation: 50 ( 2x 1+3i - y 1-2i ) = 31 + 17i Rationalizing the denominators inside the parentheses: 2x 1+3i = 2x(1-3i) (1+3i)(1-3i) = 2x(1-3i) 1^2 + 3^2 = 2x(1-3i) 10 = x(1-3i) 5 y 1-2i = y(1+2i) (1-2i)(1+2i) = y(1+2i) 1^2 + 2^2 = y(1+2i) 5 Substituting these back into the given equation: 50 ( x(1-3i) 5 - y(1+2i) 5 ) = 31 + 17i 10(x(1-3i) - y(1+2i)) = 31 + 17i 10(x - y) - 10i(3x + 2y) = 31 + 17i Equating the real and imaginary parts on both sides: 10(x - y) = 31 10x - 10y = 31 -10(3x + 2y) = 17 -30x - 20y