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Simplifying (4 + 3i)(7 + -1i) = 0 Multiply (4 + 3i) * (7 + -1i) (4(7 + -1i) + 3i * (7 + -1i)) = 0 ((7 * 4 + -1i * 4) + 3i * (7 + -1i)) = 0 ((28 + -4i) + 3i * (7 + -1i)) = 0 (28 + -4i + (7 * 3i + -1i * 3i)) = 0 (28 + -4i + (21i + -3i2)) = 0 Combine like terms: -4i + 21i = 17i (28 + 17i + -3i2) = 0 Solving 28 + 17i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -1i)(4 + 3i) = 0Subproblem 1
Set the factor '(7 + -1i)' equal to zero and attempt to solve: Simplifying 7 + -1i = 0 Solving 7 + -1i = 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 + -1i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1i = 0 + -7 -1i = 0 + -7 Combine like terms: 0 + -7 = -7 -1i = -7 Divide each side by '-1'. i = 7 Simplifying i = 7Subproblem 2
Set the factor '(4 + 3i)' equal to zero and attempt to solve: Simplifying 4 + 3i = 0 Solving 4 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3i = 0 + -4 3i = 0 + -4 Combine like terms: 0 + -4 = -4 3i = -4 Divide each side by '3'. i = -1.333333333 Simplifying i = -1.333333333Solution
i = {7, -1.333333333}
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