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Simplifying (5 + -7i)(-4 + -3i) = 0 Multiply (5 + -7i) * (-4 + -3i) (5(-4 + -3i) + -7i * (-4 + -3i)) = 0 ((-4 * 5 + -3i * 5) + -7i * (-4 + -3i)) = 0 ((-20 + -15i) + -7i * (-4 + -3i)) = 0 (-20 + -15i + (-4 * -7i + -3i * -7i)) = 0 (-20 + -15i + (28i + 21i2)) = 0 Combine like terms: -15i + 28i = 13i (-20 + 13i + 21i2) = 0 Solving -20 + 13i + 21i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + -3i)(5 + -7i) = 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 + -7i)' equal to zero and attempt to solve: Simplifying 5 + -7i = 0 Solving 5 + -7i = 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 + -7i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7i = 0 + -5 -7i = 0 + -5 Combine like terms: 0 + -5 = -5 -7i = -5 Divide each side by '-7'. i = 0.7142857143 Simplifying i = 0.7142857143Solution
i = {-1.333333333, 0.7142857143}
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