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Simplifying (3i + 7)(7i + -4) = 0 Reorder the terms: (7 + 3i)(7i + -4) = 0 Reorder the terms: (7 + 3i)(-4 + 7i) = 0 Multiply (7 + 3i) * (-4 + 7i) (7(-4 + 7i) + 3i * (-4 + 7i)) = 0 ((-4 * 7 + 7i * 7) + 3i * (-4 + 7i)) = 0 ((-28 + 49i) + 3i * (-4 + 7i)) = 0 (-28 + 49i + (-4 * 3i + 7i * 3i)) = 0 (-28 + 49i + (-12i + 21i2)) = 0 Combine like terms: 49i + -12i = 37i (-28 + 37i + 21i2) = 0 Solving -28 + 37i + 21i2 = 0 Solving for variable 'i'. Factor a trinomial. (-7 + -3i)(4 + -7i) = 0Subproblem 1
Set the factor '(-7 + -3i)' equal to zero and attempt to solve: Simplifying -7 + -3i = 0 Solving -7 + -3i = 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 + -3i = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3i = 0 + 7 -3i = 0 + 7 Combine like terms: 0 + 7 = 7 -3i = 7 Divide each side by '-3'. i = -2.333333333 Simplifying i = -2.333333333Subproblem 2
Set the factor '(4 + -7i)' equal to zero and attempt to solve: Simplifying 4 + -7i = 0 Solving 4 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7i = 0 + -4 -7i = 0 + -4 Combine like terms: 0 + -4 = -4 -7i = -4 Divide each side by '-7'. i = 0.5714285714 Simplifying i = 0.5714285714Solution
i = {-2.333333333, 0.5714285714}
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