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Simplifying (5 + 5i)(-3 + -7i) = 0 Multiply (5 + 5i) * (-3 + -7i) (5(-3 + -7i) + 5i * (-3 + -7i)) = 0 ((-3 * 5 + -7i * 5) + 5i * (-3 + -7i)) = 0 ((-15 + -35i) + 5i * (-3 + -7i)) = 0 (-15 + -35i + (-3 * 5i + -7i * 5i)) = 0 (-15 + -35i + (-15i + -35i2)) = 0 Combine like terms: -35i + -15i = -50i (-15 + -50i + -35i2) = 0 Solving -15 + -50i + -35i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-5'. -5(3 + 10i + 7i2) = 0 Factor a trinomial. -5((1 + i)(3 + 7i)) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 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 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Subproblem 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 = {-1, -0.4285714286}
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