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Simplifying (-7 + -4i)(-6 + -6i) = 0 Multiply (-7 + -4i) * (-6 + -6i) (-7(-6 + -6i) + -4i * (-6 + -6i)) = 0 ((-6 * -7 + -6i * -7) + -4i * (-6 + -6i)) = 0 ((42 + 42i) + -4i * (-6 + -6i)) = 0 (42 + 42i + (-6 * -4i + -6i * -4i)) = 0 (42 + 42i + (24i + 24i2)) = 0 Combine like terms: 42i + 24i = 66i (42 + 66i + 24i2) = 0 Solving 42 + 66i + 24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '6'. 6(7 + 11i + 4i2) = 0 Factor a trinomial. 6((7 + 4i)(1 + i)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + 4i)' equal to zero and attempt to solve: Simplifying 7 + 4i = 0 Solving 7 + 4i = 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 + 4i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4i = 0 + -7 4i = 0 + -7 Combine like terms: 0 + -7 = -7 4i = -7 Divide each side by '4'. i = -1.75 Simplifying i = -1.75Subproblem 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 = {-1.75, -1}
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