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Simplifying (7 + 5i)(-6 + 9i) = 0 Multiply (7 + 5i) * (-6 + 9i) (7(-6 + 9i) + 5i * (-6 + 9i)) = 0 ((-6 * 7 + 9i * 7) + 5i * (-6 + 9i)) = 0 ((-42 + 63i) + 5i * (-6 + 9i)) = 0 (-42 + 63i + (-6 * 5i + 9i * 5i)) = 0 (-42 + 63i + (-30i + 45i2)) = 0 Combine like terms: 63i + -30i = 33i (-42 + 33i + 45i2) = 0 Solving -42 + 33i + 45i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + 11i + 15i2) = 0 Factor a trinomial. 3((-7 + -5i)(2 + -3i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -5i)' equal to zero and attempt to solve: Simplifying -7 + -5i = 0 Solving -7 + -5i = 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 + -5i = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5i = 0 + 7 -5i = 0 + 7 Combine like terms: 0 + 7 = 7 -5i = 7 Divide each side by '-5'. i = -1.4 Simplifying i = -1.4Subproblem 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 = {-1.4, 0.6666666667}
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