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Simplifying (4 + -3i)(-5 + 4i) = 0 Multiply (4 + -3i) * (-5 + 4i) (4(-5 + 4i) + -3i * (-5 + 4i)) = 0 ((-5 * 4 + 4i * 4) + -3i * (-5 + 4i)) = 0 ((-20 + 16i) + -3i * (-5 + 4i)) = 0 (-20 + 16i + (-5 * -3i + 4i * -3i)) = 0 (-20 + 16i + (15i + -12i2)) = 0 Combine like terms: 16i + 15i = 31i (-20 + 31i + -12i2) = 0 Solving -20 + 31i + -12i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + 3i)(5 + -4i) = 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 + -4i)' equal to zero and attempt to solve: Simplifying 5 + -4i = 0 Solving 5 + -4i = 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 + -4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4i = 0 + -5 -4i = 0 + -5 Combine like terms: 0 + -5 = -5 -4i = -5 Divide each side by '-4'. i = 1.25 Simplifying i = 1.25Solution
i = {1.333333333, 1.25}
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