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Simplifying (3 + 2i)(7 + -1i) = 0 Multiply (3 + 2i) * (7 + -1i) (3(7 + -1i) + 2i * (7 + -1i)) = 0 ((7 * 3 + -1i * 3) + 2i * (7 + -1i)) = 0 ((21 + -3i) + 2i * (7 + -1i)) = 0 (21 + -3i + (7 * 2i + -1i * 2i)) = 0 (21 + -3i + (14i + -2i2)) = 0 Combine like terms: -3i + 14i = 11i (21 + 11i + -2i2) = 0 Solving 21 + 11i + -2i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -1i)(3 + 2i) = 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 '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 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 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Solution
i = {7, -1.5}
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