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Simplifying (8 + -3i)(-2 + -3i) = 0 Multiply (8 + -3i) * (-2 + -3i) (8(-2 + -3i) + -3i * (-2 + -3i)) = 0 ((-2 * 8 + -3i * 8) + -3i * (-2 + -3i)) = 0 ((-16 + -24i) + -3i * (-2 + -3i)) = 0 (-16 + -24i + (-2 * -3i + -3i * -3i)) = 0 (-16 + -24i + (6i + 9i2)) = 0 Combine like terms: -24i + 6i = -18i (-16 + -18i + 9i2) = 0 Solving -16 + -18i + 9i2 = 0 Solving for variable 'i'. Factor a trinomial. (-2 + -3i)(8 + -3i) = 0Subproblem 1
Set the factor '(-2 + -3i)' equal to zero and attempt to solve: Simplifying -2 + -3i = 0 Solving -2 + -3i = 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 + -3i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3i = 0 + 2 -3i = 0 + 2 Combine like terms: 0 + 2 = 2 -3i = 2 Divide each side by '-3'. i = -0.6666666667 Simplifying i = -0.6666666667Subproblem 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 = {-0.6666666667, 2.666666667}
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