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Simplifying (7 + -8i)(8 + -3i) = 0 Multiply (7 + -8i) * (8 + -3i) (7(8 + -3i) + -8i * (8 + -3i)) = 0 ((8 * 7 + -3i * 7) + -8i * (8 + -3i)) = 0 ((56 + -21i) + -8i * (8 + -3i)) = 0 (56 + -21i + (8 * -8i + -3i * -8i)) = 0 (56 + -21i + (-64i + 24i2)) = 0 Combine like terms: -21i + -64i = -85i (56 + -85i + 24i2) = 0 Solving 56 + -85i + 24i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -8i)(8 + -3i) = 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 '(8 + -3i)' equal to zero and attempt to solve: Simplifying 8 + -3i = 0 Solving 8 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3i = 0 + -8 -3i = 0 + -8 Combine like terms: 0 + -8 = -8 -3i = -8 Divide each side by '-3'. i = 2.666666667 Simplifying i = 2.666666667Solution
i = {0.875, 2.666666667}
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