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Simplifying 3 + -1(4 + -1i) + -4i(-2 + 5i) = 0 3 + (4 * -1 + -1i * -1) + -4i(-2 + 5i) = 0 3 + (-4 + 1i) + -4i(-2 + 5i) = 0 3 + -4 + 1i + (-2 * -4i + 5i * -4i) = 0 3 + -4 + 1i + (8i + -20i2) = 0 Combine like terms: 3 + -4 = -1 -1 + 1i + 8i + -20i2 = 0 Combine like terms: 1i + 8i = 9i -1 + 9i + -20i2 = 0 Solving -1 + 9i + -20i2 = 0 Solving for variable 'i'. Factor a trinomial. (-1 + 4i)(1 + -5i) = 0Subproblem 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 '(1 + -5i)' equal to zero and attempt to solve: Simplifying 1 + -5i = 0 Solving 1 + -5i = 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 + -5i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5i = 0 + -1 -5i = 0 + -1 Combine like terms: 0 + -1 = -1 -5i = -1 Divide each side by '-5'. i = 0.2 Simplifying i = 0.2Solution
i = {0.25, 0.2}
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