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Simplifying (6 + -4i)(8 + -7i) = 0 Multiply (6 + -4i) * (8 + -7i) (6(8 + -7i) + -4i * (8 + -7i)) = 0 ((8 * 6 + -7i * 6) + -4i * (8 + -7i)) = 0 ((48 + -42i) + -4i * (8 + -7i)) = 0 (48 + -42i + (8 * -4i + -7i * -4i)) = 0 (48 + -42i + (-32i + 28i2)) = 0 Combine like terms: -42i + -32i = -74i (48 + -74i + 28i2) = 0 Solving 48 + -74i + 28i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -37i + 14i2) = 0 Factor a trinomial. 2((8 + -7i)(3 + -2i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -7i)' equal to zero and attempt to solve: Simplifying 8 + -7i = 0 Solving 8 + -7i = 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 + -7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7i = 0 + -8 -7i = 0 + -8 Combine like terms: 0 + -8 = -8 -7i = -8 Divide each side by '-7'. i = 1.142857143 Simplifying i = 1.142857143Subproblem 2
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Solution
i = {1.142857143, 1.5}
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