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Simplifying (7 + 2i)(-3 + -4i) = 0 Multiply (7 + 2i) * (-3 + -4i) (7(-3 + -4i) + 2i * (-3 + -4i)) = 0 ((-3 * 7 + -4i * 7) + 2i * (-3 + -4i)) = 0 ((-21 + -28i) + 2i * (-3 + -4i)) = 0 (-21 + -28i + (-3 * 2i + -4i * 2i)) = 0 (-21 + -28i + (-6i + -8i2)) = 0 Combine like terms: -28i + -6i = -34i (-21 + -34i + -8i2) = 0 Solving -21 + -34i + -8i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 34i + 8i2) = 0 Factor a trinomial. -1((7 + 2i)(3 + 4i)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 2i)' equal to zero and attempt to solve: Simplifying 7 + 2i = 0 Solving 7 + 2i = 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 + 2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2i = 0 + -7 2i = 0 + -7 Combine like terms: 0 + -7 = -7 2i = -7 Divide each side by '2'. i = -3.5 Simplifying i = -3.5Subproblem 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 = {-3.5, -0.75}
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