Question

Solve for X and Y 3x+(2 x-y)i = 6-3i

Answer 1

x = 2 and y = 7

Explanation:

`\text{Two complex numbers are equal when they have equal real parts}\\\text{ and equal imaginary parts}\\\\a+bi=c+di\iff a=c\ and\ b=d`

`3x+(2x-y)i=6-3i\iff3x=6\ \wedge\ 2x-y=-3\\\\3x=6\qquad\text{divide both sides by 3}\\\\\boxed{x=2}\\\\\text{Put the value of x to the second equation:}\\\\2(2)-y=-3\\\\4-y=-3\qquad\text{subtract 4 from both sides}\\\\-y=-7\qquad\text{change the signs}\\\\\boxed{y=7}`