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Simplifying (3 + 4i)(7 + 8i) = 0 Multiply (3 + 4i) * (7 + 8i) (3(7 + 8i) + 4i * (7 + 8i)) = 0 ((7 * 3 + 8i * 3) + 4i * (7 + 8i)) = 0 ((21 + 24i) + 4i * (7 + 8i)) = 0 (21 + 24i + (7 * 4i + 8i * 4i)) = 0 (21 + 24i + (28i + 32i2)) = 0 Combine like terms: 24i + 28i = 52i (21 + 52i + 32i2) = 0 Solving 21 + 52i + 32i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + 8i)(3 + 4i) = 0Subproblem 1
Set the factor '(7 + 8i)' equal to zero and attempt to solve: Simplifying 7 + 8i = 0 Solving 7 + 8i = 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 + 8i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 8i = 0 + -7 8i = 0 + -7 Combine like terms: 0 + -7 = -7 8i = -7 Divide each side by '8'. i = -0.875 Simplifying i = -0.875Subproblem 2
Set the factor '(3 + 4i)' equal to zero and attempt to solve: Simplifying 3 + 4i = 0 Solving 3 + 4i = 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 + 4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4i = 0 + -3 4i = 0 + -3 Combine like terms: 0 + -3 = -3 4i = -3 Divide each side by '4'. i = -0.75 Simplifying i = -0.75Solution
i = {-0.875, -0.75}
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