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Simplifying -1(5 + 7i)(5 + 7i) = 0 Multiply (5 + 7i) * (5 + 7i) -1(5(5 + 7i) + 7i * (5 + 7i)) = 0 -1((5 * 5 + 7i * 5) + 7i * (5 + 7i)) = 0 -1((25 + 35i) + 7i * (5 + 7i)) = 0 -1(25 + 35i + (5 * 7i + 7i * 7i)) = 0 -1(25 + 35i + (35i + 49i2)) = 0 Combine like terms: 35i + 35i = 70i -1(25 + 70i + 49i2) = 0 (25 * -1 + 70i * -1 + 49i2 * -1) = 0 (-25 + -70i + -49i2) = 0 Solving -25 + -70i + -49i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 70i + 49i2) = 0 Factor a trinomial. -1((5 + 7i)(5 + 7i)) = 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 '(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 = -0.7142857143Solution
i = {-0.7142857143, -0.7142857143}
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