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Simplifying (-10 + -2i)(2 + 7i) = 0 Multiply (-10 + -2i) * (2 + 7i) (-10(2 + 7i) + -2i * (2 + 7i)) = 0 ((2 * -10 + 7i * -10) + -2i * (2 + 7i)) = 0 ((-20 + -70i) + -2i * (2 + 7i)) = 0 (-20 + -70i + (2 * -2i + 7i * -2i)) = 0 (-20 + -70i + (-4i + -14i2)) = 0 Combine like terms: -70i + -4i = -74i (-20 + -74i + -14i2) = 0 Solving -20 + -74i + -14i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-2'. -2(10 + 37i + 7i2) = 0 Factor a trinomial. -2((5 + i)(2 + 7i)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + i)' equal to zero and attempt to solve: Simplifying 5 + i = 0 Solving 5 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + i = 0 + -5 i = 0 + -5 Combine like terms: 0 + -5 = -5 i = -5 Simplifying i = -5Subproblem 2
Set the factor '(2 + 7i)' equal to zero and attempt to solve: Simplifying 2 + 7i = 0 Solving 2 + 7i = 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 + 7i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7i = 0 + -2 7i = 0 + -2 Combine like terms: 0 + -2 = -2 7i = -2 Divide each side by '7'. i = -0.2857142857 Simplifying i = -0.2857142857Solution
i = {-5, -0.2857142857}
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