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Simplifying (8 + -7i)(6 + -3i) = 0 Multiply (8 + -7i) * (6 + -3i) (8(6 + -3i) + -7i * (6 + -3i)) = 0 ((6 * 8 + -3i * 8) + -7i * (6 + -3i)) = 0 ((48 + -24i) + -7i * (6 + -3i)) = 0 (48 + -24i + (6 * -7i + -3i * -7i)) = 0 (48 + -24i + (-42i + 21i2)) = 0 Combine like terms: -24i + -42i = -66i (48 + -66i + 21i2) = 0 Solving 48 + -66i + 21i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(16 + -22i + 7i2) = 0 Factor a trinomial. 3((8 + -7i)(2 + -1i)) = 0 Ignore the factor 3.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 '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Solution
i = {1.142857143, 2}
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