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Find the values of x and y for which the complex numbers
(2x+3y)+i(2y-1) and 10+i(5-x) are equal.
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Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.
It gives you two equations
2x + 3y = 10, (1)
2y-1 = 5-x. (2)
From (2), express x = 5 - 2y + 1 = 6 - 2y and substitute it into (1). You will get
2*(6-2y) + 3y = 10,
12 - 4y + 3y = 10,
-y = 10 - 12,
-y = -2,
y = 2.
Then x = 6 - 2y = 6 - 2*2 = 6 - 4 = 2.
Answer. x = 2, y = 2.
