Find all the solutions for x

Question

Find x and y so that the following equation is true. (Enter your answers as a comma-separated list.)

(x² − 2x) + y²i = 8 + (6y − 9)i

Answer 1

In setting up this problem, I don't think any thought was given that there could be a complex x and complex y contributing to the imaginary and real term, respectively.

Thus, the desired solution was to be found using

x² - 2x = 8

y² = 6y - 9

x² - 2x - 8 = 0 (x - 4)(x+2) = 0 x = 4, -2

y² - 6y + 9 = 0 (y +3)² = 0 y = -3

Solutions are (-2, -3), (4, -3)