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Simplifying (4 + -7i)(-3 + 6i) = 0 Multiply (4 + -7i) * (-3 + 6i) (4(-3 + 6i) + -7i * (-3 + 6i)) = 0 ((-3 * 4 + 6i * 4) + -7i * (-3 + 6i)) = 0 ((-12 + 24i) + -7i * (-3 + 6i)) = 0 (-12 + 24i + (-3 * -7i + 6i * -7i)) = 0 (-12 + 24i + (21i + -42i2)) = 0 Combine like terms: 24i + 21i = 45i (-12 + 45i + -42i2) = 0 Solving -12 + 45i + -42i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 15i + -14i2) = 0 Factor a trinomial. 3((-4 + 7i)(1 + -2i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 7i)' equal to zero and attempt to solve: Simplifying -4 + 7i = 0 Solving -4 + 7i = 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 + 7i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7i = 0 + 4 7i = 0 + 4 Combine like terms: 0 + 4 = 4 7i = 4 Divide each side by '7'. i = 0.5714285714 Simplifying i = 0.5714285714Subproblem 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 = {0.5714285714, 0.5}
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