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Simplifying (7 + -7i)(1 + -3i) = 0 Multiply (7 + -7i) * (1 + -3i) (7(1 + -3i) + -7i * (1 + -3i)) = 0 ((1 * 7 + -3i * 7) + -7i * (1 + -3i)) = 0 ((7 + -21i) + -7i * (1 + -3i)) = 0 (7 + -21i + (1 * -7i + -3i * -7i)) = 0 (7 + -21i + (-7i + 21i2)) = 0 Combine like terms: -21i + -7i = -28i (7 + -28i + 21i2) = 0 Solving 7 + -28i + 21i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '7'. 7(1 + -4i + 3i2) = 0 Factor a trinomial. 7((1 + -3i)(1 + -1i)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Subproblem 2
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 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 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Solution
i = {0.3333333333, 1}
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