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Simplifying (3 + 7i)(-5 + -2i) = 0 Multiply (3 + 7i) * (-5 + -2i) (3(-5 + -2i) + 7i * (-5 + -2i)) = 0 ((-5 * 3 + -2i * 3) + 7i * (-5 + -2i)) = 0 ((-15 + -6i) + 7i * (-5 + -2i)) = 0 (-15 + -6i + (-5 * 7i + -2i * 7i)) = 0 (-15 + -6i + (-35i + -14i2)) = 0 Combine like terms: -6i + -35i = -41i (-15 + -41i + -14i2) = 0 Solving -15 + -41i + -14i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 41i + 14i2) = 0 Factor a trinomial. -1((5 + 2i)(3 + 7i)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 2i)' equal to zero and attempt to solve: Simplifying 5 + 2i = 0 Solving 5 + 2i = 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 + 2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2i = 0 + -5 2i = 0 + -5 Combine like terms: 0 + -5 = -5 2i = -5 Divide each side by '2'. i = -2.5 Simplifying i = -2.5Subproblem 2
Set the factor '(3 + 7i)' equal to zero and attempt to solve: Simplifying 3 + 7i = 0 Solving 3 + 7i = 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 + 7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7i = 0 + -3 7i = 0 + -3 Combine like terms: 0 + -3 = -3 7i = -3 Divide each side by '7'. i = -0.4285714286 Simplifying i = -0.4285714286Solution
i = {-2.5, -0.4285714286}
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