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Simplifying (-1 + 3i)(4 + 5i) = 0 Multiply (-1 + 3i) * (4 + 5i) (-1(4 + 5i) + 3i * (4 + 5i)) = 0 ((4 * -1 + 5i * -1) + 3i * (4 + 5i)) = 0 ((-4 + -5i) + 3i * (4 + 5i)) = 0 (-4 + -5i + (4 * 3i + 5i * 3i)) = 0 (-4 + -5i + (12i + 15i2)) = 0 Combine like terms: -5i + 12i = 7i (-4 + 7i + 15i2) = 0 Solving -4 + 7i + 15i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + -5i)(1 + -3i) = 0Subproblem 1
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 = -0.8Subproblem 2
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Solution
i = {-0.8, 0.3333333333}
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