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Simplifying (2 + 9i)(-2 + 3i) = 0 Multiply (2 + 9i) * (-2 + 3i) (2(-2 + 3i) + 9i * (-2 + 3i)) = 0 ((-2 * 2 + 3i * 2) + 9i * (-2 + 3i)) = 0 ((-4 + 6i) + 9i * (-2 + 3i)) = 0 (-4 + 6i + (-2 * 9i + 3i * 9i)) = 0 (-4 + 6i + (-18i + 27i2)) = 0 Combine like terms: 6i + -18i = -12i (-4 + -12i + 27i2) = 0 Solving -4 + -12i + 27i2 = 0 Solving for variable 'i'. Factor a trinomial. (-2 + -9i)(2 + -3i) = 0Subproblem 1
Set the factor '(-2 + -9i)' equal to zero and attempt to solve: Simplifying -2 + -9i = 0 Solving -2 + -9i = 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 + -9i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -9i = 0 + 2 -9i = 0 + 2 Combine like terms: 0 + 2 = 2 -9i = 2 Divide each side by '-9'. i = -0.2222222222 Simplifying i = -0.2222222222Subproblem 2
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 = 0.6666666667Solution
i = {-0.2222222222, 0.6666666667}
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