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Simplifying (-5 + 7i)(2 + -6i) = 0 Multiply (-5 + 7i) * (2 + -6i) (-5(2 + -6i) + 7i * (2 + -6i)) = 0 ((2 * -5 + -6i * -5) + 7i * (2 + -6i)) = 0 ((-10 + 30i) + 7i * (2 + -6i)) = 0 (-10 + 30i + (2 * 7i + -6i * 7i)) = 0 (-10 + 30i + (14i + -42i2)) = 0 Combine like terms: 30i + 14i = 44i (-10 + 44i + -42i2) = 0 Solving -10 + 44i + -42i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 22i + -21i2) = 0 Factor a trinomial. 2((-5 + 7i)(1 + -3i)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.7142857143Subproblem 2
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Solution
i = {0.7142857143, 0.3333333333}
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