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Simplifying (x + -1iy)(x + -1iy) = 0 Reorder the terms: (-1iy + x)(x + -1iy) = 0 Reorder the terms: (-1iy + x)(-1iy + x) = 0 Multiply (-1iy + x) * (-1iy + x) (-1iy * (-1iy + x) + x(-1iy + x)) = 0 ((-1iy * -1iy + x * -1iy) + x(-1iy + x)) = 0 Reorder the terms: ((-1ixy + 1i2y2) + x(-1iy + x)) = 0 ((-1ixy + 1i2y2) + x(-1iy + x)) = 0 (-1ixy + 1i2y2 + (-1iy * x + x * x)) = 0 (-1ixy + 1i2y2 + (-1ixy + x2)) = 0 Reorder the terms: (-1ixy + -1ixy + 1i2y2 + x2) = 0 Combine like terms: -1ixy + -1ixy = -2ixy (-2ixy + 1i2y2 + x2) = 0 Solving -2ixy + 1i2y2 + x2 = 0 Solving for variable 'i'. Factor a trinomial. (iy + -1x)(iy + -1x) = 0Subproblem 1
Set the factor '(iy + -1x)' equal to zero and attempt to solve: Simplifying iy + -1x = 0 Solving iy + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. iy + -1x + x = 0 + x Combine like terms: -1x + x = 0 iy + 0 = 0 + x iy = 0 + x Remove the zero: iy = x Divide each side by 'y'. i = xy-1 Simplifying i = xy-1Subproblem 2
Set the factor '(iy + -1x)' equal to zero and attempt to solve: Simplifying iy + -1x = 0 Solving iy + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. iy + -1x + x = 0 + x Combine like terms: -1x + x = 0 iy + 0 = 0 + x iy = 0 + x Remove the zero: iy = x Divide each side by 'y'. i = xy-1 Simplifying i = xy-1Solution
i = {xy-1, xy-1}
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