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Simplifying (4 + -5i)(12 + 11i) = 0 Multiply (4 + -5i) * (12 + 11i) (4(12 + 11i) + -5i * (12 + 11i)) = 0 ((12 * 4 + 11i * 4) + -5i * (12 + 11i)) = 0 ((48 + 44i) + -5i * (12 + 11i)) = 0 (48 + 44i + (12 * -5i + 11i * -5i)) = 0 (48 + 44i + (-60i + -55i2)) = 0 Combine like terms: 44i + -60i = -16i (48 + -16i + -55i2) = 0 Solving 48 + -16i + -55i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -5i)(12 + 11i) = 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 '(12 + 11i)' equal to zero and attempt to solve: Simplifying 12 + 11i = 0 Solving 12 + 11i = 0 Move all terms containing i to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 11i = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 11i = 0 + -12 11i = 0 + -12 Combine like terms: 0 + -12 = -12 11i = -12 Divide each side by '11'. i = -1.090909091 Simplifying i = -1.090909091Solution
i = {0.8, -1.090909091}
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