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Simplifying (5 + -4i)(7 + 2i) = 0 Multiply (5 + -4i) * (7 + 2i) (5(7 + 2i) + -4i * (7 + 2i)) = 0 ((7 * 5 + 2i * 5) + -4i * (7 + 2i)) = 0 ((35 + 10i) + -4i * (7 + 2i)) = 0 (35 + 10i + (7 * -4i + 2i * -4i)) = 0 (35 + 10i + (-28i + -8i2)) = 0 Combine like terms: 10i + -28i = -18i (35 + -18i + -8i2) = 0 Solving 35 + -18i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -4i)(7 + 2i) = 0Subproblem 1
Set the factor '(5 + -4i)' equal to zero and attempt to solve: Simplifying 5 + -4i = 0 Solving 5 + -4i = 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 + -4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4i = 0 + -5 -4i = 0 + -5 Combine like terms: 0 + -5 = -5 -4i = -5 Divide each side by '-4'. i = 1.25 Simplifying i = 1.25Subproblem 2
Set the factor '(7 + 2i)' equal to zero and attempt to solve: Simplifying 7 + 2i = 0 Solving 7 + 2i = 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 + 2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2i = 0 + -7 2i = 0 + -7 Combine like terms: 0 + -7 = -7 2i = -7 Divide each side by '2'. i = -3.5 Simplifying i = -3.5Solution
i = {1.25, -3.5}
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