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Simplifying (7 + 11i)(8 + -11i) = 0 Multiply (7 + 11i) * (8 + -11i) (7(8 + -11i) + 11i * (8 + -11i)) = 0 ((8 * 7 + -11i * 7) + 11i * (8 + -11i)) = 0 ((56 + -77i) + 11i * (8 + -11i)) = 0 (56 + -77i + (8 * 11i + -11i * 11i)) = 0 (56 + -77i + (88i + -121i2)) = 0 Combine like terms: -77i + 88i = 11i (56 + 11i + -121i2) = 0 Solving 56 + 11i + -121i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + -11i)(7 + 11i) = 0Subproblem 1
Set the factor '(8 + -11i)' equal to zero and attempt to solve: Simplifying 8 + -11i = 0 Solving 8 + -11i = 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 + -11i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -11i = 0 + -8 -11i = 0 + -8 Combine like terms: 0 + -8 = -8 -11i = -8 Divide each side by '-11'. i = 0.7272727273 Simplifying i = 0.7272727273Subproblem 2
Set the factor '(7 + 11i)' equal to zero and attempt to solve: Simplifying 7 + 11i = 0 Solving 7 + 11i = 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 + 11i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 11i = 0 + -7 11i = 0 + -7 Combine like terms: 0 + -7 = -7 11i = -7 Divide each side by '11'. i = -0.6363636364 Simplifying i = -0.6363636364Solution
i = {0.7272727273, -0.6363636364}
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