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Simplifying (6 + -4i)(-4 + 5i) = 0 Multiply (6 + -4i) * (-4 + 5i) (6(-4 + 5i) + -4i * (-4 + 5i)) = 0 ((-4 * 6 + 5i * 6) + -4i * (-4 + 5i)) = 0 ((-24 + 30i) + -4i * (-4 + 5i)) = 0 (-24 + 30i + (-4 * -4i + 5i * -4i)) = 0 (-24 + 30i + (16i + -20i2)) = 0 Combine like terms: 30i + 16i = 46i (-24 + 46i + -20i2) = 0 Solving -24 + 46i + -20i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 23i + -10i2) = 0 Factor a trinomial. 2((-3 + 2i)(4 + -5i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 2i)' equal to zero and attempt to solve: Simplifying -3 + 2i = 0 Solving -3 + 2i = 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 + 2i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2i = 0 + 3 2i = 0 + 3 Combine like terms: 0 + 3 = 3 2i = 3 Divide each side by '2'. i = 1.5 Simplifying i = 1.5Subproblem 2
Set the factor '(4 + -5i)' equal to zero and attempt to solve: Simplifying 4 + -5i = 0 Solving 4 + -5i = 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 + -5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5i = 0 + -4 -5i = 0 + -4 Combine like terms: 0 + -4 = -4 -5i = -4 Divide each side by '-5'. i = 0.8 Simplifying i = 0.8Solution
i = {1.5, 0.8}
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