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Simplifying (1 + -1i)(6 + 5i) = 0 Multiply (1 + -1i) * (6 + 5i) (1(6 + 5i) + -1i * (6 + 5i)) = 0 ((6 * 1 + 5i * 1) + -1i * (6 + 5i)) = 0 ((6 + 5i) + -1i * (6 + 5i)) = 0 (6 + 5i + (6 * -1i + 5i * -1i)) = 0 (6 + 5i + (-6i + -5i2)) = 0 Combine like terms: 5i + -6i = -1i (6 + -1i + -5i2) = 0 Solving 6 + -1i + -5i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + -1i)(6 + 5i) = 0Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Subproblem 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 = {1, -1.2}
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