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Simplifying (7 + 6i)(-3 + -3i) = 0 Multiply (7 + 6i) * (-3 + -3i) (7(-3 + -3i) + 6i * (-3 + -3i)) = 0 ((-3 * 7 + -3i * 7) + 6i * (-3 + -3i)) = 0 ((-21 + -21i) + 6i * (-3 + -3i)) = 0 (-21 + -21i + (-3 * 6i + -3i * 6i)) = 0 (-21 + -21i + (-18i + -18i2)) = 0 Combine like terms: -21i + -18i = -39i (-21 + -39i + -18i2) = 0 Solving -21 + -39i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-3'. -3(7 + 13i + 6i2) = 0 Factor a trinomial. -3((7 + 6i)(1 + i)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(7 + 6i)' equal to zero and attempt to solve: Simplifying 7 + 6i = 0 Solving 7 + 6i = 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 + 6i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6i = 0 + -7 6i = 0 + -7 Combine like terms: 0 + -7 = -7 6i = -7 Divide each side by '6'. i = -1.166666667 Simplifying i = -1.166666667Subproblem 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 = {-1.166666667, -1}
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