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Simplifying (-4i + 3)(-1i + -12) = 0 Reorder the terms: (3 + -4i)(-1i + -12) = 0 Reorder the terms: (3 + -4i)(-12 + -1i) = 0 Multiply (3 + -4i) * (-12 + -1i) (3(-12 + -1i) + -4i * (-12 + -1i)) = 0 ((-12 * 3 + -1i * 3) + -4i * (-12 + -1i)) = 0 ((-36 + -3i) + -4i * (-12 + -1i)) = 0 (-36 + -3i + (-12 * -4i + -1i * -4i)) = 0 (-36 + -3i + (48i + 4i2)) = 0 Combine like terms: -3i + 48i = 45i (-36 + 45i + 4i2) = 0 Solving -36 + 45i + 4i2 = 0 Solving for variable 'i'. Factor a trinomial. (-12 + -1i)(3 + -4i) = 0Subproblem 1
Set the factor '(-12 + -1i)' equal to zero and attempt to solve: Simplifying -12 + -1i = 0 Solving -12 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1i = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1i = 0 + 12 -1i = 0 + 12 Combine like terms: 0 + 12 = 12 -1i = 12 Divide each side by '-1'. i = -12 Simplifying i = -12Subproblem 2
Set the factor '(3 + -4i)' equal to zero and attempt to solve: Simplifying 3 + -4i = 0 Solving 3 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4i = 0 + -3 -4i = 0 + -3 Combine like terms: 0 + -3 = -3 -4i = -3 Divide each side by '-4'. i = 0.75 Simplifying i = 0.75Solution
i = {-12, 0.75}
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