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Simplifying (-2 + -8i)(8 + -7i) = 0 Multiply (-2 + -8i) * (8 + -7i) (-2(8 + -7i) + -8i * (8 + -7i)) = 0 ((8 * -2 + -7i * -2) + -8i * (8 + -7i)) = 0 ((-16 + 14i) + -8i * (8 + -7i)) = 0 (-16 + 14i + (8 * -8i + -7i * -8i)) = 0 (-16 + 14i + (-64i + 56i2)) = 0 Combine like terms: 14i + -64i = -50i (-16 + -50i + 56i2) = 0 Solving -16 + -50i + 56i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -25i + 28i2) = 0 Factor a trinomial. 2((-1 + -4i)(8 + -7i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -4i)' equal to zero and attempt to solve: Simplifying -1 + -4i = 0 Solving -1 + -4i = 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 + -4i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4i = 0 + 1 -4i = 0 + 1 Combine like terms: 0 + 1 = 1 -4i = 1 Divide each side by '-4'. i = -0.25 Simplifying i = -0.25Subproblem 2
Set the factor '(8 + -7i)' equal to zero and attempt to solve: Simplifying 8 + -7i = 0 Solving 8 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7i = 0 + -8 -7i = 0 + -8 Combine like terms: 0 + -8 = -8 -7i = -8 Divide each side by '-7'. i = 1.142857143 Simplifying i = 1.142857143Solution
i = {-0.25, 1.142857143}
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