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Simplifying (4 + -6i)(2 + -5i) = 0 Multiply (4 + -6i) * (2 + -5i) (4(2 + -5i) + -6i * (2 + -5i)) = 0 ((2 * 4 + -5i * 4) + -6i * (2 + -5i)) = 0 ((8 + -20i) + -6i * (2 + -5i)) = 0 (8 + -20i + (2 * -6i + -5i * -6i)) = 0 (8 + -20i + (-12i + 30i2)) = 0 Combine like terms: -20i + -12i = -32i (8 + -32i + 30i2) = 0 Solving 8 + -32i + 30i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -16i + 15i2) = 0 Factor a trinomial. 2((2 + -5i)(2 + -3i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -5i)' equal to zero and attempt to solve: Simplifying 2 + -5i = 0 Solving 2 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5i = 0 + -2 -5i = 0 + -2 Combine like terms: 0 + -2 = -2 -5i = -2 Divide each side by '-5'. i = 0.4 Simplifying i = 0.4Subproblem 2
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Solution
i = {0.4, 0.6666666667}
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