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Simplifying (4 + -1i)(5 + 6i) = 0 Multiply (4 + -1i) * (5 + 6i) (4(5 + 6i) + -1i * (5 + 6i)) = 0 ((5 * 4 + 6i * 4) + -1i * (5 + 6i)) = 0 ((20 + 24i) + -1i * (5 + 6i)) = 0 (20 + 24i + (5 * -1i + 6i * -1i)) = 0 (20 + 24i + (-5i + -6i2)) = 0 Combine like terms: 24i + -5i = 19i (20 + 19i + -6i2) = 0 Solving 20 + 19i + -6i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -1i)(5 + 6i) = 0Subproblem 1
Set the factor '(4 + -1i)' equal to zero and attempt to solve: Simplifying 4 + -1i = 0 Solving 4 + -1i = 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 + -1i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i = 0 + -4 -1i = 0 + -4 Combine like terms: 0 + -4 = -4 -1i = -4 Divide each side by '-1'. i = 4 Simplifying i = 4Subproblem 2
Set the factor '(5 + 6i)' equal to zero and attempt to solve: Simplifying 5 + 6i = 0 Solving 5 + 6i = 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 + 6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6i = 0 + -5 6i = 0 + -5 Combine like terms: 0 + -5 = -5 6i = -5 Divide each side by '6'. i = -0.8333333333 Simplifying i = -0.8333333333Solution
i = {4, -0.8333333333}
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