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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. (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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