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Simplifying (2 + -3i)(5 + 7i) = 0 Multiply (2 + -3i) * (5 + 7i) (2(5 + 7i) + -3i * (5 + 7i)) = 0 ((5 * 2 + 7i * 2) + -3i * (5 + 7i)) = 0 ((10 + 14i) + -3i * (5 + 7i)) = 0 (10 + 14i + (5 * -3i + 7i * -3i)) = 0 (10 + 14i + (-15i + -21i2)) = 0 Combine like terms: 14i + -15i = -1i (10 + -1i + -21i2) = 0 Solving 10 + -1i + -21i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -3i)(5 + 7i) = 0Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Subproblem 2
Set the factor '(5 + 7i)' equal to zero and attempt to solve: Simplifying 5 + 7i = 0 Solving 5 + 7i = 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 + 7i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7i = 0 + -5 7i = 0 + -5 Combine like terms: 0 + -5 = -5 7i = -5 Divide each side by '7'. i = -0.7142857143 Simplifying i = -0.7142857143Solution
i = {0.6666666667, -0.7142857143}
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