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Simplifying (3 + -2i)(1 + 7i) = 0 Multiply (3 + -2i) * (1 + 7i) (3(1 + 7i) + -2i * (1 + 7i)) = 0 ((1 * 3 + 7i * 3) + -2i * (1 + 7i)) = 0 ((3 + 21i) + -2i * (1 + 7i)) = 0 (3 + 21i + (1 * -2i + 7i * -2i)) = 0 (3 + 21i + (-2i + -14i2)) = 0 Combine like terms: 21i + -2i = 19i (3 + 19i + -14i2) = 0 Solving 3 + 19i + -14i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -2i)(1 + 7i) = 0Subproblem 1
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 = 1.5Subproblem 2
Set the factor '(1 + 7i)' equal to zero and attempt to solve: Simplifying 1 + 7i = 0 Solving 1 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 7i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7i = 0 + -1 7i = 0 + -1 Combine like terms: 0 + -1 = -1 7i = -1 Divide each side by '7'. i = -0.1428571429 Simplifying i = -0.1428571429Solution
i = {1.5, -0.1428571429}
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