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