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Simplifying (2 + -3i)(4 + 5i) = 0 Multiply (2 + -3i) * (4 + 5i) (2(4 + 5i) + -3i * (4 + 5i)) = 0 ((4 * 2 + 5i * 2) + -3i * (4 + 5i)) = 0 ((8 + 10i) + -3i * (4 + 5i)) = 0 (8 + 10i + (4 * -3i + 5i * -3i)) = 0 (8 + 10i + (-12i + -15i2)) = 0 Combine like terms: 10i + -12i = -2i (8 + -2i + -15i2) = 0 Solving 8 + -2i + -15i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -3i)(4 + 5i) = 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 '(4 + 5i)' equal to zero and attempt to solve: Simplifying 4 + 5i = 0 Solving 4 + 5i = 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 + 5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 0 + -4 5i = 0 + -4 Combine like terms: 0 + -4 = -4 5i = -4 Divide each side by '5'. i = -0.8 Simplifying i = -0.8Solution
i = {0.6666666667, -0.8}
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