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Simplifying (8 + -2i)(2 + 5i) = 0 Multiply (8 + -2i) * (2 + 5i) (8(2 + 5i) + -2i * (2 + 5i)) = 0 ((2 * 8 + 5i * 8) + -2i * (2 + 5i)) = 0 ((16 + 40i) + -2i * (2 + 5i)) = 0 (16 + 40i + (2 * -2i + 5i * -2i)) = 0 (16 + 40i + (-4i + -10i2)) = 0 Combine like terms: 40i + -4i = 36i (16 + 36i + -10i2) = 0 Solving 16 + 36i + -10i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 18i + -5i2) = 0 Factor a trinomial. 2((4 + -1i)(2 + 5i)) = 0 Ignore the factor 2.Subproblem 1
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 = 4Subproblem 2
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 = -0.4Solution
i = {4, -0.4}
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