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Simplifying (7 + -2i)(3 + i) = 0 Multiply (7 + -2i) * (3 + i) (7(3 + i) + -2i * (3 + i)) = 0 ((3 * 7 + i * 7) + -2i * (3 + i)) = 0 ((21 + 7i) + -2i * (3 + i)) = 0 (21 + 7i + (3 * -2i + i * -2i)) = 0 (21 + 7i + (-6i + -2i2)) = 0 Combine like terms: 7i + -6i = 1i (21 + 1i + -2i2) = 0 Solving 21 + 1i + -2i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -2i)(3 + i) = 0Subproblem 1
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 = 3.5Subproblem 2
Set the factor '(3 + i)' equal to zero and attempt to solve: Simplifying 3 + i = 0 Solving 3 + i = 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 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3Solution
i = {3.5, -3}
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