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Simplifying (7 + -5i)(3 + -8i) = 0 Multiply (7 + -5i) * (3 + -8i) (7(3 + -8i) + -5i * (3 + -8i)) = 0 ((3 * 7 + -8i * 7) + -5i * (3 + -8i)) = 0 ((21 + -56i) + -5i * (3 + -8i)) = 0 (21 + -56i + (3 * -5i + -8i * -5i)) = 0 (21 + -56i + (-15i + 40i2)) = 0 Combine like terms: -56i + -15i = -71i (21 + -71i + 40i2) = 0 Solving 21 + -71i + 40i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -8i)(7 + -5i) = 0Subproblem 1
Set the factor '(3 + -8i)' equal to zero and attempt to solve: Simplifying 3 + -8i = 0 Solving 3 + -8i = 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 + -8i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8i = 0 + -3 -8i = 0 + -3 Combine like terms: 0 + -3 = -3 -8i = -3 Divide each side by '-8'. i = 0.375 Simplifying i = 0.375Subproblem 2
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 = 1.4Solution
i = {0.375, 1.4}
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