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Simplifying (-6 + 9i)(7 + i) = 0 Multiply (-6 + 9i) * (7 + i) (-6(7 + i) + 9i * (7 + i)) = 0 ((7 * -6 + i * -6) + 9i * (7 + i)) = 0 ((-42 + -6i) + 9i * (7 + i)) = 0 (-42 + -6i + (7 * 9i + i * 9i)) = 0 (-42 + -6i + (63i + 9i2)) = 0 Combine like terms: -6i + 63i = 57i (-42 + 57i + 9i2) = 0 Solving -42 + 57i + 9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + 19i + 3i2) = 0 Factor a trinomial. 3((-7 + -1i)(2 + -3i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -1i)' equal to zero and attempt to solve: Simplifying -7 + -1i = 0 Solving -7 + -1i = 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 + -1i = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1i = 0 + 7 -1i = 0 + 7 Combine like terms: 0 + 7 = 7 -1i = 7 Divide each side by '-1'. i = -7 Simplifying i = -7Subproblem 2
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Solution
i = {-7, 0.6666666667}
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