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Simplifying 0 = (3 + 7i)(8 + -2i) Multiply (3 + 7i) * (8 + -2i) 0 = (3(8 + -2i) + 7i * (8 + -2i)) 0 = ((8 * 3 + -2i * 3) + 7i * (8 + -2i)) 0 = ((24 + -6i) + 7i * (8 + -2i)) 0 = (24 + -6i + (8 * 7i + -2i * 7i)) 0 = (24 + -6i + (56i + -14i2)) Combine like terms: -6i + 56i = 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((-3 + -7i)(4 + -1i)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.4285714286Subproblem 2
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 = 4Solution
i = {-0.4285714286, 4}
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