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With x, y real, find the values of x and y in each case by equating real and imaginary parts: (a) (x + 2y) + i(2x - 3y) = 5 - 4i (b) (x + iy) + (7 - 5i) = 9 + 4i (c) x² - y² - i(2x + y) = 2i

1. (a) x=1, y=2; (b) x=2, y=9; (c) x=0, y=-2 (or x=0, y=... per real constraint)
2. (a) x=2, y=1; (b) x=2, y=9; (c) x=1, y=1
3. (a) x=1, y=2; (b) x=2, y=-1; (c) x=2, y=-2
4. (a) x=3, y=1; (b) x=9, y=4; (c) x=0, y=0

Correct answer: (a) x=1, y=2; (b) x=2, y=9; (c) x=0, y=-2 (or x=0, y=... per real constraint)

Solution

Equating real and imaginary parts converts each complex equation into a pair of linear (or quadratic) equations in x and y, which are solved simultaneously.

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