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Simplifying (6 + 2i)(7 + -5i) = 0 Multiply (6 + 2i) * (7 + -5i) (6(7 + -5i) + 2i * (7 + -5i)) = 0 ((7 * 6 + -5i * 6) + 2i * (7 + -5i)) = 0 ((42 + -30i) + 2i * (7 + -5i)) = 0 (42 + -30i + (7 * 2i + -5i * 2i)) = 0 (42 + -30i + (14i + -10i2)) = 0 Combine like terms: -30i + 14i = -16i (42 + -16i + -10i2) = 0 Solving 42 + -16i + -10i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + -8i + -5i2) = 0 Factor a trinomial. 2((7 + -5i)(3 + i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -5i)' equal to zero and attempt to solve: Simplifying 7 + -5i = 0 Solving 7 + -5i = 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 + -5i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5i = 0 + -7 -5i = 0 + -7 Combine like terms: 0 + -7 = -7 -5i = -7 Divide each side by '-5'. i = 1.4 Simplifying i = 1.4Subproblem 2
Set the factor '(3 + i)' equal to zero and attempt to solve: Simplifying 3 + i = 0 Solving 3 + i = 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 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3Solution
i = {1.4, -3}
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