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Simplifying (2 + 5xi)(7 + -1xi) = 0 Multiply (2 + 5ix) * (7 + -1ix) (2(7 + -1ix) + 5ix * (7 + -1ix)) = 0 ((7 * 2 + -1ix * 2) + 5ix * (7 + -1ix)) = 0 ((14 + -2ix) + 5ix * (7 + -1ix)) = 0 (14 + -2ix + (7 * 5ix + -1ix * 5ix)) = 0 (14 + -2ix + (35ix + -5i2x2)) = 0 Combine like terms: -2ix + 35ix = 33ix (14 + 33ix + -5i2x2) = 0 Solving 14 + 33ix + -5i2x2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -1ix)(2 + 5ix) = 0Subproblem 1
Set the factor '(7 + -1ix)' equal to zero and attempt to solve: Simplifying 7 + -1ix = 0 Solving 7 + -1ix = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1ix = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1ix = 0 + -7 -1ix = 0 + -7 Combine like terms: 0 + -7 = -7 -1ix = -7 Divide each side by '-1x'. i = 7x-1 Simplifying i = 7x-1Subproblem 2
Set the factor '(2 + 5ix)' equal to zero and attempt to solve: Simplifying 2 + 5ix = 0 Solving 2 + 5ix = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5ix = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5ix = 0 + -2 5ix = 0 + -2 Combine like terms: 0 + -2 = -2 5ix = -2 Divide each side by '5x'. i = -0.4x-1 Simplifying i = -0.4x-1Solution
i = {7x-1, -0.4x-1}
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