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Simplifying (2 + 3i)(-3 + 4i) = 0 Multiply (2 + 3i) * (-3 + 4i) (2(-3 + 4i) + 3i * (-3 + 4i)) = 0 ((-3 * 2 + 4i * 2) + 3i * (-3 + 4i)) = 0 ((-6 + 8i) + 3i * (-3 + 4i)) = 0 (-6 + 8i + (-3 * 3i + 4i * 3i)) = 0 (-6 + 8i + (-9i + 12i2)) = 0 Combine like terms: 8i + -9i = -1i (-6 + -1i + 12i2) = 0 Solving -6 + -1i + 12i2 = 0 Solving for variable 'i'. Factor a trinomial. (-2 + -3i)(3 + -4i) = 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 '(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 = {-0.6666666667, 0.75}
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