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Simplifying (3 + -5i)(-8 + 2i) = 0 Multiply (3 + -5i) * (-8 + 2i) (3(-8 + 2i) + -5i * (-8 + 2i)) = 0 ((-8 * 3 + 2i * 3) + -5i * (-8 + 2i)) = 0 ((-24 + 6i) + -5i * (-8 + 2i)) = 0 (-24 + 6i + (-8 * -5i + 2i * -5i)) = 0 (-24 + 6i + (40i + -10i2)) = 0 Combine like terms: 6i + 40i = 46i (-24 + 46i + -10i2) = 0 Solving -24 + 46i + -10i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 23i + -5i2) = 0 Factor a trinomial. 2((-4 + i)(3 + -5i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + i)' equal to zero and attempt to solve: Simplifying -4 + i = 0 Solving -4 + i = 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 + i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + i = 0 + 4 i = 0 + 4 Combine like terms: 0 + 4 = 4 i = 4 Simplifying i = 4Subproblem 2
Set the factor '(3 + -5i)' equal to zero and attempt to solve: Simplifying 3 + -5i = 0 Solving 3 + -5i = 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 + -5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5i = 0 + -3 -5i = 0 + -3 Combine like terms: 0 + -3 = -3 -5i = -3 Divide each side by '-5'. i = 0.6 Simplifying i = 0.6Solution
i = {4, 0.6}
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