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Simplifying (-1x + 2i)(x + -2i) = 0 Reorder the terms: (2i + -1x)(x + -2i) = 0 Reorder the terms: (2i + -1x)(-2i + x) = 0 Multiply (2i + -1x) * (-2i + x) (2i * (-2i + x) + -1x * (-2i + x)) = 0 ((-2i * 2i + x * 2i) + -1x * (-2i + x)) = 0 Reorder the terms: ((2ix + -4i2) + -1x * (-2i + x)) = 0 ((2ix + -4i2) + -1x * (-2i + x)) = 0 (2ix + -4i2 + (-2i * -1x + x * -1x)) = 0 (2ix + -4i2 + (2ix + -1x2)) = 0 Reorder the terms: (2ix + 2ix + -4i2 + -1x2) = 0 Combine like terms: 2ix + 2ix = 4ix (4ix + -4i2 + -1x2) = 0 Solving 4ix + -4i2 + -1x2 = 0 Solving for variable 'i'. Factor a trinomial. (-2i + x)(2i + -1x) = 0Subproblem 1
Set the factor '(-2i + x)' equal to zero and attempt to solve: Simplifying -2i + x = 0 Solving -2i + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. -2i + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 -2i + 0 = 0 + -1x -2i = 0 + -1x Remove the zero: -2i = -1x Divide each side by '-2'. i = 0.5x Simplifying i = 0.5xSubproblem 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 = {0.5x, 0.5x}
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