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Simplifying (8 + -3i)(2 + 7i) = 0 Multiply (8 + -3i) * (2 + 7i) (8(2 + 7i) + -3i * (2 + 7i)) = 0 ((2 * 8 + 7i * 8) + -3i * (2 + 7i)) = 0 ((16 + 56i) + -3i * (2 + 7i)) = 0 (16 + 56i + (2 * -3i + 7i * -3i)) = 0 (16 + 56i + (-6i + -21i2)) = 0 Combine like terms: 56i + -6i = 50i (16 + 50i + -21i2) = 0 Solving 16 + 50i + -21i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + -3i)(2 + 7i) = 0Subproblem 1
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 = 2.666666667Subproblem 2
Set the factor '(2 + 7i)' equal to zero and attempt to solve: Simplifying 2 + 7i = 0 Solving 2 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7i = 0 + -2 7i = 0 + -2 Combine like terms: 0 + -2 = -2 7i = -2 Divide each side by '7'. i = -0.2857142857 Simplifying i = -0.2857142857Solution
i = {2.666666667, -0.2857142857}
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