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Simplifying (6 + -3i)(7 + -2i) = 0 Multiply (6 + -3i) * (7 + -2i) (6(7 + -2i) + -3i * (7 + -2i)) = 0 ((7 * 6 + -2i * 6) + -3i * (7 + -2i)) = 0 ((42 + -12i) + -3i * (7 + -2i)) = 0 (42 + -12i + (7 * -3i + -2i * -3i)) = 0 (42 + -12i + (-21i + 6i2)) = 0 Combine like terms: -12i + -21i = -33i (42 + -33i + 6i2) = 0 Solving 42 + -33i + 6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + -11i + 2i2) = 0 Factor a trinomial. 3((2 + -1i)(7 + -2i)) = 0 Ignore the factor 3.Subproblem 1
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 = 2Subproblem 2
Set the factor '(7 + -2i)' equal to zero and attempt to solve: Simplifying 7 + -2i = 0 Solving 7 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2i = 0 + -7 -2i = 0 + -7 Combine like terms: 0 + -7 = -7 -2i = -7 Divide each side by '-2'. i = 3.5 Simplifying i = 3.5Solution
i = {2, 3.5}
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