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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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