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Simplifying (-3 + 6i)(4 + -5i) = 0 Multiply (-3 + 6i) * (4 + -5i) (-3(4 + -5i) + 6i * (4 + -5i)) = 0 ((4 * -3 + -5i * -3) + 6i * (4 + -5i)) = 0 ((-12 + 15i) + 6i * (4 + -5i)) = 0 (-12 + 15i + (4 * 6i + -5i * 6i)) = 0 (-12 + 15i + (24i + -30i2)) = 0 Combine like terms: 15i + 24i = 39i (-12 + 39i + -30i2) = 0 Solving -12 + 39i + -30i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 13i + -10i2) = 0 Factor a trinomial. 3((-4 + 5i)(1 + -2i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 5i)' equal to zero and attempt to solve: Simplifying -4 + 5i = 0 Solving -4 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 5i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5i = 0 + 4 5i = 0 + 4 Combine like terms: 0 + 4 = 4 5i = 4 Divide each side by '5'. i = 0.8 Simplifying i = 0.8Subproblem 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 = {0.8, 0.5}
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