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Simplifying (7 + -28i)(4 + -1i) = 0 Multiply (7 + -28i) * (4 + -1i) (7(4 + -1i) + -28i * (4 + -1i)) = 0 ((4 * 7 + -1i * 7) + -28i * (4 + -1i)) = 0 ((28 + -7i) + -28i * (4 + -1i)) = 0 (28 + -7i + (4 * -28i + -1i * -28i)) = 0 (28 + -7i + (-112i + 28i2)) = 0 Combine like terms: -7i + -112i = -119i (28 + -119i + 28i2) = 0 Solving 28 + -119i + 28i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '7'. 7(4 + -17i + 4i2) = 0 Factor a trinomial. 7((1 + -4i)(4 + -1i)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + -4i)' equal to zero and attempt to solve: Simplifying 1 + -4i = 0 Solving 1 + -4i = 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 + -4i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4i = 0 + -1 -4i = 0 + -1 Combine like terms: 0 + -1 = -1 -4i = -1 Divide each side by '-4'. i = 0.25 Simplifying i = 0.25Subproblem 2
Set the factor '(4 + -1i)' equal to zero and attempt to solve: Simplifying 4 + -1i = 0 Solving 4 + -1i = 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 + -1i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i = 0 + -4 -1i = 0 + -4 Combine like terms: 0 + -4 = -4 -1i = -4 Divide each side by '-1'. i = 4 Simplifying i = 4Solution
i = {0.25, 4}
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