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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 = -9i (-42 + -9i + 6i2) = 0 Solving -42 + -9i + 6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + -3i + 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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