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Simplifying (2 + -5i)(6 + -3i) = 0 Multiply (2 + -5i) * (6 + -3i) (2(6 + -3i) + -5i * (6 + -3i)) = 0 ((6 * 2 + -3i * 2) + -5i * (6 + -3i)) = 0 ((12 + -6i) + -5i * (6 + -3i)) = 0 (12 + -6i + (6 * -5i + -3i * -5i)) = 0 (12 + -6i + (-30i + 15i2)) = 0 Combine like terms: -6i + -30i = -36i (12 + -36i + 15i2) = 0 Solving 12 + -36i + 15i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -12i + 5i2) = 0 Factor a trinomial. 3((2 + -5i)(2 + -1i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -5i)' equal to zero and attempt to solve: Simplifying 2 + -5i = 0 Solving 2 + -5i = 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 + -5i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5i = 0 + -2 -5i = 0 + -2 Combine like terms: 0 + -2 = -2 -5i = -2 Divide each side by '-5'. i = 0.4 Simplifying i = 0.4Subproblem 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 = {0.4, 2}
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