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Simplifying (-4 + -3i)(6 + -7i) = 0 Multiply (-4 + -3i) * (6 + -7i) (-4(6 + -7i) + -3i * (6 + -7i)) = 0 ((6 * -4 + -7i * -4) + -3i * (6 + -7i)) = 0 ((-24 + 28i) + -3i * (6 + -7i)) = 0 (-24 + 28i + (6 * -3i + -7i * -3i)) = 0 (-24 + 28i + (-18i + 21i2)) = 0 Combine like terms: 28i + -18i = 10i (-24 + 10i + 21i2) = 0 Solving -24 + 10i + 21i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + -3i)(6 + -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 '(6 + -7i)' equal to zero and attempt to solve: Simplifying 6 + -7i = 0 Solving 6 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7i = 0 + -6 -7i = 0 + -6 Combine like terms: 0 + -6 = -6 -7i = -6 Divide each side by '-7'. i = 0.8571428571 Simplifying i = 0.8571428571Solution
i = {-1.333333333, 0.8571428571}
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