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Simplifying 0 = (8 + 2i)(3 + -7i) Multiply (8 + 2i) * (3 + -7i) 0 = (8(3 + -7i) + 2i * (3 + -7i)) 0 = ((3 * 8 + -7i * 8) + 2i * (3 + -7i)) 0 = ((24 + -56i) + 2i * (3 + -7i)) 0 = (24 + -56i + (3 * 2i + -7i * 2i)) 0 = (24 + -56i + (6i + -14i2)) Combine like terms: -56i + 6i = -50i 0 = (24 + -50i + -14i2) Solving 0 = 24 + -50i + -14i2 Solving for variable 'i'. Combine like terms: 0 + -24 = -24 -24 + 50i + 14i2 = 24 + -50i + -14i2 + -24 + 50i + 14i2 Reorder the terms: -24 + 50i + 14i2 = 24 + -24 + -50i + 50i + -14i2 + 14i2 Combine like terms: 24 + -24 = 0 -24 + 50i + 14i2 = 0 + -50i + 50i + -14i2 + 14i2 -24 + 50i + 14i2 = -50i + 50i + -14i2 + 14i2 Combine like terms: -50i + 50i = 0 -24 + 50i + 14i2 = 0 + -14i2 + 14i2 -24 + 50i + 14i2 = -14i2 + 14i2 Combine like terms: -14i2 + 14i2 = 0 -24 + 50i + 14i2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 25i + 7i2) = 0 Factor a trinomial. 2((-4 + -1i)(3 + -7i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1i)' equal to zero and attempt to solve: Simplifying -4 + -1i = 0 Solving -4 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1i = 0 + 4 -1i = 0 + 4 Combine like terms: 0 + 4 = 4 -1i = 4 Divide each side by '-1'. i = -4 Simplifying i = -4Subproblem 2
Set the factor '(3 + -7i)' equal to zero and attempt to solve: Simplifying 3 + -7i = 0 Solving 3 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7i = 0 + -3 -7i = 0 + -3 Combine like terms: 0 + -3 = -3 -7i = -3 Divide each side by '-7'. i = 0.4285714286 Simplifying i = 0.4285714286Solution
i = {-4, 0.4285714286}
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