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Simplifying (x + -1i)(x + -2i) = 0 Reorder the terms: (-1i + x)(x + -2i) = 0 Reorder the terms: (-1i + x)(-2i + x) = 0 Multiply (-1i + x) * (-2i + x) (-1i * (-2i + x) + x(-2i + x)) = 0 ((-2i * -1i + x * -1i) + x(-2i + x)) = 0 Reorder the terms: ((-1ix + 2i2) + x(-2i + x)) = 0 ((-1ix + 2i2) + x(-2i + x)) = 0 (-1ix + 2i2 + (-2i * x + x * x)) = 0 (-1ix + 2i2 + (-2ix + x2)) = 0 Reorder the terms: (-1ix + -2ix + 2i2 + x2) = 0 Combine like terms: -1ix + -2ix = -3ix (-3ix + 2i2 + x2) = 0 Solving -3ix + 2i2 + x2 = 0 Solving for variable 'i'. Factor a trinomial. (i + -1x)(2i + -1x) = 0Subproblem 1
Set the factor '(i + -1x)' equal to zero and attempt to solve: Simplifying i + -1x = 0 Solving i + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. i + -1x + x = 0 + x Combine like terms: -1x + x = 0 i + 0 = 0 + x i = 0 + x Remove the zero: i = x Simplifying i = xSubproblem 2
Set the factor '(2i + -1x)' equal to zero and attempt to solve: Simplifying 2i + -1x = 0 Solving 2i + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. 2i + -1x + x = 0 + x Combine like terms: -1x + x = 0 2i + 0 = 0 + x 2i = 0 + x Remove the zero: 2i = x Divide each side by '2'. i = 0.5x Simplifying i = 0.5xSolution
i = {x, 0.5x}
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