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Simplifying (x + iy)(x + -1iy) = 1989 Reorder the terms: (iy + x)(x + -1iy) = 1989 Reorder the terms: (iy + x)(-1iy + x) = 1989 Multiply (iy + x) * (-1iy + x) (iy(-1iy + x) + x(-1iy + x)) = 1989 ((-1iy * iy + x * iy) + x(-1iy + x)) = 1989 Reorder the terms: ((ixy + -1i2y2) + x(-1iy + x)) = 1989 ((ixy + -1i2y2) + x(-1iy + x)) = 1989 (ixy + -1i2y2 + (-1iy * x + x * x)) = 1989 (ixy + -1i2y2 + (-1ixy + x2)) = 1989 Reorder the terms: (ixy + -1ixy + -1i2y2 + x2) = 1989 Combine like terms: ixy + -1ixy = 0 (0 + -1i2y2 + x2) = 1989 (-1i2y2 + x2) = 1989 Solving -1i2y2 + x2 = 1989 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1x2' to each side of the equation. -1i2y2 + x2 + -1x2 = 1989 + -1x2 Combine like terms: x2 + -1x2 = 0 -1i2y2 + 0 = 1989 + -1x2 -1i2y2 = 1989 + -1x2 Divide each side by '-1y2'. i2 = -1989y-2 + x2y-2 Simplifying i2 = -1989y-2 + x2y-2 Reorder the terms: i2 = x2y-2 + -1989y-2 Reorder the terms: i2 + -1x2y-2 + 1989y-2 = x2y-2 + -1x2y-2 + -1989y-2 + 1989y-2 Combine like terms: x2y-2 + -1x2y-2 = 0 i2 + -1x2y-2 + 1989y-2 = 0 + -1989y-2 + 1989y-2 i2 + -1x2y-2 + 1989y-2 = -1989y-2 + 1989y-2 Combine like terms: -1989y-2 + 1989y-2 = 0 i2 + -1x2y-2 + 1989y-2 = 0 The solution to this equation could not be determined.
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