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Simplifying (3 + 8i)(7 + -9i) = 0 Multiply (3 + 8i) * (7 + -9i) (3(7 + -9i) + 8i * (7 + -9i)) = 0 ((7 * 3 + -9i * 3) + 8i * (7 + -9i)) = 0 ((21 + -27i) + 8i * (7 + -9i)) = 0 (21 + -27i + (7 * 8i + -9i * 8i)) = 0 (21 + -27i + (56i + -72i2)) = 0 Combine like terms: -27i + 56i = 29i (21 + 29i + -72i2) = 0 Solving 21 + 29i + -72i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -9i)(3 + 8i) = 0Subproblem 1
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 = 0.7777777778Subproblem 2
Set the factor '(3 + 8i)' equal to zero and attempt to solve: Simplifying 3 + 8i = 0 Solving 3 + 8i = 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 + 8i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8i = 0 + -3 8i = 0 + -3 Combine like terms: 0 + -3 = -3 8i = -3 Divide each side by '8'. i = -0.375 Simplifying i = -0.375Solution
i = {0.7777777778, -0.375}
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