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Simplifying (5 + -2i)(4 + -3i) = 0 Multiply (5 + -2i) * (4 + -3i) (5(4 + -3i) + -2i * (4 + -3i)) = 0 ((4 * 5 + -3i * 5) + -2i * (4 + -3i)) = 0 ((20 + -15i) + -2i * (4 + -3i)) = 0 (20 + -15i + (4 * -2i + -3i * -2i)) = 0 (20 + -15i + (-8i + 6i2)) = 0 Combine like terms: -15i + -8i = -23i (20 + -23i + 6i2) = 0 Solving 20 + -23i + 6i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -3i)(5 + -2i) = 0Subproblem 1
Set the factor '(4 + -3i)' equal to zero and attempt to solve: Simplifying 4 + -3i = 0 Solving 4 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3i = 0 + -4 -3i = 0 + -4 Combine like terms: 0 + -4 = -4 -3i = -4 Divide each side by '-3'. i = 1.333333333 Simplifying i = 1.333333333Subproblem 2
Set the factor '(5 + -2i)' equal to zero and attempt to solve: Simplifying 5 + -2i = 0 Solving 5 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i = 0 + -5 -2i = 0 + -5 Combine like terms: 0 + -5 = -5 -2i = -5 Divide each side by '-2'. i = 2.5 Simplifying i = 2.5Solution
i = {1.333333333, 2.5}
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