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Simplifying (2 + -1i)(-3 + 6i) = 0 Multiply (2 + -1i) * (-3 + 6i) (2(-3 + 6i) + -1i * (-3 + 6i)) = 0 ((-3 * 2 + 6i * 2) + -1i * (-3 + 6i)) = 0 ((-6 + 12i) + -1i * (-3 + 6i)) = 0 (-6 + 12i + (-3 * -1i + 6i * -1i)) = 0 (-6 + 12i + (3i + -6i2)) = 0 Combine like terms: 12i + 3i = 15i (-6 + 15i + -6i2) = 0 Solving -6 + 15i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 5i + -2i2) = 0 Factor a trinomial. 3((-2 + i)(1 + -2i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + i)' equal to zero and attempt to solve: Simplifying -2 + i = 0 Solving -2 + i = 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 + i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + i = 0 + 2 i = 0 + 2 Combine like terms: 0 + 2 = 2 i = 2 Simplifying i = 2Subproblem 2
Set the factor '(1 + -2i)' equal to zero and attempt to solve: Simplifying 1 + -2i = 0 Solving 1 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2i = 0 + -1 -2i = 0 + -1 Combine like terms: 0 + -1 = -1 -2i = -1 Divide each side by '-2'. i = 0.5 Simplifying i = 0.5Solution
i = {2, 0.5}
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