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Simplifying (8 + -2i)(8 + -7i) = 0 Multiply (8 + -2i) * (8 + -7i) (8(8 + -7i) + -2i * (8 + -7i)) = 0 ((8 * 8 + -7i * 8) + -2i * (8 + -7i)) = 0 ((64 + -56i) + -2i * (8 + -7i)) = 0 (64 + -56i + (8 * -2i + -7i * -2i)) = 0 (64 + -56i + (-16i + 14i2)) = 0 Combine like terms: -56i + -16i = -72i (64 + -72i + 14i2) = 0 Solving 64 + -72i + 14i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(32 + -36i + 7i2) = 0 Factor a trinomial. 2((8 + -7i)(4 + -1i)) = 0 Ignore the factor 2.Subproblem 1
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 = 1.142857143Subproblem 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 = {1.142857143, 4}
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