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Simplifying (-7 + -9i)(3 + i) = 0 Multiply (-7 + -9i) * (3 + i) (-7(3 + i) + -9i * (3 + i)) = 0 ((3 * -7 + i * -7) + -9i * (3 + i)) = 0 ((-21 + -7i) + -9i * (3 + i)) = 0 (-21 + -7i + (3 * -9i + i * -9i)) = 0 (-21 + -7i + (-27i + -9i2)) = 0 Combine like terms: -7i + -27i = -34i (-21 + -34i + -9i2) = 0 Solving -21 + -34i + -9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 34i + 9i2) = 0 Factor a trinomial. -1((3 + i)(7 + 9i)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + i)' equal to zero and attempt to solve: Simplifying 3 + i = 0 Solving 3 + i = 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 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3Subproblem 2
Set the factor '(7 + 9i)' equal to zero and attempt to solve: Simplifying 7 + 9i = 0 Solving 7 + 9i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 9i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9i = 0 + -7 9i = 0 + -7 Combine like terms: 0 + -7 = -7 9i = -7 Divide each side by '9'. i = -0.7777777778 Simplifying i = -0.7777777778Solution
i = {-3, -0.7777777778}
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