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Simplifying (6 + -1i)(5 + 4i) = 0 Multiply (6 + -1i) * (5 + 4i) (6(5 + 4i) + -1i * (5 + 4i)) = 0 ((5 * 6 + 4i * 6) + -1i * (5 + 4i)) = 0 ((30 + 24i) + -1i * (5 + 4i)) = 0 (30 + 24i + (5 * -1i + 4i * -1i)) = 0 (30 + 24i + (-5i + -4i2)) = 0 Combine like terms: 24i + -5i = 19i (30 + 19i + -4i2) = 0 Solving 30 + 19i + -4i2 = 0 Solving for variable 'i'. Factor a trinomial. (6 + -1i)(5 + 4i) = 0Subproblem 1
Set the factor '(6 + -1i)' equal to zero and attempt to solve: Simplifying 6 + -1i = 0 Solving 6 + -1i = 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 + -1i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1i = 0 + -6 -1i = 0 + -6 Combine like terms: 0 + -6 = -6 -1i = -6 Divide each side by '-1'. i = 6 Simplifying i = 6Subproblem 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 = {6, -1.25}
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