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Simplifying (1 + i)(7 + -3i) = 0 Multiply (1 + i) * (7 + -3i) (1(7 + -3i) + i(7 + -3i)) = 0 ((7 * 1 + -3i * 1) + i(7 + -3i)) = 0 ((7 + -3i) + i(7 + -3i)) = 0 (7 + -3i + (7 * i + -3i * i)) = 0 (7 + -3i + (7i + -3i2)) = 0 Combine like terms: -3i + 7i = 4i (7 + 4i + -3i2) = 0 Solving 7 + 4i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -3i)(1 + i) = 0Subproblem 1
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 = 2.333333333Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 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 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {2.333333333, -1}
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