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Simplifying (4 + -5i)(6 + -5i) = 0 Multiply (4 + -5i) * (6 + -5i) (4(6 + -5i) + -5i * (6 + -5i)) = 0 ((6 * 4 + -5i * 4) + -5i * (6 + -5i)) = 0 ((24 + -20i) + -5i * (6 + -5i)) = 0 (24 + -20i + (6 * -5i + -5i * -5i)) = 0 (24 + -20i + (-30i + 25i2)) = 0 Combine like terms: -20i + -30i = -50i (24 + -50i + 25i2) = 0 Solving 24 + -50i + 25i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -5i)(6 + -5i) = 0Subproblem 1
Set the factor '(4 + -5i)' equal to zero and attempt to solve: Simplifying 4 + -5i = 0 Solving 4 + -5i = 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 + -5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5i = 0 + -4 -5i = 0 + -4 Combine like terms: 0 + -4 = -4 -5i = -4 Divide each side by '-5'. i = 0.8 Simplifying i = 0.8Subproblem 2
Set the factor '(6 + -5i)' equal to zero and attempt to solve: Simplifying 6 + -5i = 0 Solving 6 + -5i = 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 + -5i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5i = 0 + -6 -5i = 0 + -6 Combine like terms: 0 + -6 = -6 -5i = -6 Divide each side by '-5'. i = 1.2 Simplifying i = 1.2Solution
i = {0.8, 1.2}
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