Answer:
(x, y) = (17/31, 1/31)
Step-by-step explanation:
Simplify the given equation, then equate real parts and equate imaginary parts. This will give you two equations in the two unknowns.
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simplify
(5 -3i)(x -yi) = 3(x +2yi) +1 -2i
5x -5yi -3xi +3yi² = 3x +6yi +1 -2i
(5x -3y) +i(-5y -3x) = (3x +1) +i(6y -2)
equate real, imaginary parts
This resolves to the two equations ...
- 5x -3y = 3x +1
- -5y -3x = 6y -2
solve the system
Putting these equations into general form gives ...
2x -3y -1 = 0
3x +11y -2 = 0
Using the "cross multiplication method" to solve these equations, we get ...
x = ((-3)(-2) -(11)(-1))/(2(11) -3(-3)) = 17/31
y = ((-1)(3) -(-2)(2))/31 = 1/31
The values of x and y that satisfy this equation are ...
(x, y) = (17/31, 1/31)
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You can read more about the cross multiplication method here.
https://brainly.com/question/26397343
