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Simplifying (8 + -7i)(7 + -3i) = 0 Multiply (8 + -7i) * (7 + -3i) (8(7 + -3i) + -7i * (7 + -3i)) = 0 ((7 * 8 + -3i * 8) + -7i * (7 + -3i)) = 0 ((56 + -24i) + -7i * (7 + -3i)) = 0 (56 + -24i + (7 * -7i + -3i * -7i)) = 0 (56 + -24i + (-49i + 21i2)) = 0 Combine like terms: -24i + -49i = -73i (56 + -73i + 21i2) = 0 Solving 56 + -73i + 21i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + -7i)(7 + -3i) = 0Subproblem 1
Set the factor '(8 + -7i)' equal to zero and attempt to solve: Simplifying 8 + -7i = 0 Solving 8 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7i = 0 + -8 -7i = 0 + -8 Combine like terms: 0 + -8 = -8 -7i = -8 Divide each side by '-7'. i = 1.142857143 Simplifying i = 1.142857143Subproblem 2
Set the factor '(7 + -3i)' equal to zero and attempt to solve: Simplifying 7 + -3i = 0 Solving 7 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3i = 0 + -7 -3i = 0 + -7 Combine like terms: 0 + -7 = -7 -3i = -7 Divide each side by '-3'. i = 2.333333333 Simplifying i = 2.333333333Solution
i = {1.142857143, 2.333333333}
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