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Simplifying (7 + -6i)(-7 + -2i) = 0 Multiply (7 + -6i) * (-7 + -2i) (7(-7 + -2i) + -6i * (-7 + -2i)) = 0 ((-7 * 7 + -2i * 7) + -6i * (-7 + -2i)) = 0 ((-49 + -14i) + -6i * (-7 + -2i)) = 0 (-49 + -14i + (-7 * -6i + -2i * -6i)) = 0 (-49 + -14i + (42i + 12i2)) = 0 Combine like terms: -14i + 42i = 28i (-49 + 28i + 12i2) = 0 Solving -49 + 28i + 12i2 = 0 Solving for variable 'i'. Factor a trinomial. (-7 + -2i)(7 + -6i) = 0Subproblem 1
Set the factor '(-7 + -2i)' equal to zero and attempt to solve: Simplifying -7 + -2i = 0 Solving -7 + -2i = 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 + -2i = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2i = 0 + 7 -2i = 0 + 7 Combine like terms: 0 + 7 = 7 -2i = 7 Divide each side by '-2'. i = -3.5 Simplifying i = -3.5Subproblem 2
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 = 1.166666667Solution
i = {-3.5, 1.166666667}
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