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Simplifying (5 + 7i)(-3 + -5i) = 0 Multiply (5 + 7i) * (-3 + -5i) (5(-3 + -5i) + 7i * (-3 + -5i)) = 0 ((-3 * 5 + -5i * 5) + 7i * (-3 + -5i)) = 0 ((-15 + -25i) + 7i * (-3 + -5i)) = 0 (-15 + -25i + (-3 * 7i + -5i * 7i)) = 0 (-15 + -25i + (-21i + -35i2)) = 0 Combine like terms: -25i + -21i = -46i (-15 + -46i + -35i2) = 0 Solving -15 + -46i + -35i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 46i + 35i2) = 0 Factor a trinomial. -1((5 + 7i)(3 + 5i)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 7i)' equal to zero and attempt to solve: Simplifying 5 + 7i = 0 Solving 5 + 7i = 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 + 7i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7i = 0 + -5 7i = 0 + -5 Combine like terms: 0 + -5 = -5 7i = -5 Divide each side by '7'. i = -0.7142857143 Simplifying i = -0.7142857143Subproblem 2
Set the factor '(3 + 5i)' equal to zero and attempt to solve: Simplifying 3 + 5i = 0 Solving 3 + 5i = 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 + 5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5i = 0 + -3 5i = 0 + -3 Combine like terms: 0 + -3 = -3 5i = -3 Divide each side by '5'. i = -0.6 Simplifying i = -0.6Solution
i = {-0.7142857143, -0.6}
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