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Simplifying (7 + 3i)(3 + -7i) = 0 Multiply (7 + 3i) * (3 + -7i) (7(3 + -7i) + 3i * (3 + -7i)) = 0 ((3 * 7 + -7i * 7) + 3i * (3 + -7i)) = 0 ((21 + -49i) + 3i * (3 + -7i)) = 0 (21 + -49i + (3 * 3i + -7i * 3i)) = 0 (21 + -49i + (9i + -21i2)) = 0 Combine like terms: -49i + 9i = -40i (21 + -40i + -21i2) = 0 Solving 21 + -40i + -21i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -7i)(7 + 3i) = 0Subproblem 1
Set the factor '(3 + -7i)' equal to zero and attempt to solve: Simplifying 3 + -7i = 0 Solving 3 + -7i = 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 + -7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7i = 0 + -3 -7i = 0 + -3 Combine like terms: 0 + -3 = -3 -7i = -3 Divide each side by '-7'. i = 0.4285714286 Simplifying i = 0.4285714286Subproblem 2
Set the factor '(7 + 3i)' equal to zero and attempt to solve: Simplifying 7 + 3i = 0 Solving 7 + 3i = 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 + 3i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3i = 0 + -7 3i = 0 + -7 Combine like terms: 0 + -7 = -7 3i = -7 Divide each side by '3'. i = -2.333333333 Simplifying i = -2.333333333Solution
i = {0.4285714286, -2.333333333}
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