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Simplifying (-6 + 2i)(-2 + -5i) = 0 Multiply (-6 + 2i) * (-2 + -5i) (-6(-2 + -5i) + 2i * (-2 + -5i)) = 0 ((-2 * -6 + -5i * -6) + 2i * (-2 + -5i)) = 0 ((12 + 30i) + 2i * (-2 + -5i)) = 0 (12 + 30i + (-2 * 2i + -5i * 2i)) = 0 (12 + 30i + (-4i + -10i2)) = 0 Combine like terms: 30i + -4i = 26i (12 + 26i + -10i2) = 0 Solving 12 + 26i + -10i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 13i + -5i2) = 0 Factor a trinomial. 2((3 + -1i)(2 + 5i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1i)' equal to zero and attempt to solve: Simplifying 3 + -1i = 0 Solving 3 + -1i = 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 + -1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1i = 0 + -3 -1i = 0 + -3 Combine like terms: 0 + -3 = -3 -1i = -3 Divide each side by '-1'. i = 3 Simplifying i = 3Subproblem 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 = {3, -0.4}
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