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Simplifying (4 + -3i)(10 + -7i) = 0 Multiply (4 + -3i) * (10 + -7i) (4(10 + -7i) + -3i * (10 + -7i)) = 0 ((10 * 4 + -7i * 4) + -3i * (10 + -7i)) = 0 ((40 + -28i) + -3i * (10 + -7i)) = 0 (40 + -28i + (10 * -3i + -7i * -3i)) = 0 (40 + -28i + (-30i + 21i2)) = 0 Combine like terms: -28i + -30i = -58i (40 + -58i + 21i2) = 0 Solving 40 + -58i + 21i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -3i)(10 + -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 '(10 + -7i)' equal to zero and attempt to solve: Simplifying 10 + -7i = 0 Solving 10 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -7i = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7i = 0 + -10 -7i = 0 + -10 Combine like terms: 0 + -10 = -10 -7i = -10 Divide each side by '-7'. i = 1.428571429 Simplifying i = 1.428571429Solution
i = {1.333333333, 1.428571429}
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