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Simplifying (7 + -8i)(3 + 4i) = 0 Multiply (7 + -8i) * (3 + 4i) (7(3 + 4i) + -8i * (3 + 4i)) = 0 ((3 * 7 + 4i * 7) + -8i * (3 + 4i)) = 0 ((21 + 28i) + -8i * (3 + 4i)) = 0 (21 + 28i + (3 * -8i + 4i * -8i)) = 0 (21 + 28i + (-24i + -32i2)) = 0 Combine like terms: 28i + -24i = 4i (21 + 4i + -32i2) = 0 Solving 21 + 4i + -32i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -8i)(3 + 4i) = 0Subproblem 1
Set the factor '(7 + -8i)' equal to zero and attempt to solve: Simplifying 7 + -8i = 0 Solving 7 + -8i = 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 + -8i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8i = 0 + -7 -8i = 0 + -7 Combine like terms: 0 + -7 = -7 -8i = -7 Divide each side by '-8'. i = 0.875 Simplifying i = 0.875Subproblem 2
Set the factor '(3 + 4i)' equal to zero and attempt to solve: Simplifying 3 + 4i = 0 Solving 3 + 4i = 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 + 4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4i = 0 + -3 4i = 0 + -3 Combine like terms: 0 + -3 = -3 4i = -3 Divide each side by '4'. i = -0.75 Simplifying i = -0.75Solution
i = {0.875, -0.75}
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