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Simplifying (2 + -5i)(2 + -6i) = 0 Multiply (2 + -5i) * (2 + -6i) (2(2 + -6i) + -5i * (2 + -6i)) = 0 ((2 * 2 + -6i * 2) + -5i * (2 + -6i)) = 0 ((4 + -12i) + -5i * (2 + -6i)) = 0 (4 + -12i + (2 * -5i + -6i * -5i)) = 0 (4 + -12i + (-10i + 30i2)) = 0 Combine like terms: -12i + -10i = -22i (4 + -22i + 30i2) = 0 Solving 4 + -22i + 30i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -11i + 15i2) = 0 Factor a trinomial. 2((1 + -3i)(2 + -5i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Subproblem 2
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 = 0.4Solution
i = {0.3333333333, 0.4}
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