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Simplifying (4 + -5i)(5 + -1i) = 0 Multiply (4 + -5i) * (5 + -1i) (4(5 + -1i) + -5i * (5 + -1i)) = 0 ((5 * 4 + -1i * 4) + -5i * (5 + -1i)) = 0 ((20 + -4i) + -5i * (5 + -1i)) = 0 (20 + -4i + (5 * -5i + -1i * -5i)) = 0 (20 + -4i + (-25i + 5i2)) = 0 Combine like terms: -4i + -25i = -29i (20 + -29i + 5i2) = 0 Solving 20 + -29i + 5i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -5i)(5 + -1i) = 0Subproblem 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 '(5 + -1i)' equal to zero and attempt to solve: Simplifying 5 + -1i = 0 Solving 5 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1i = 0 + -5 -1i = 0 + -5 Combine like terms: 0 + -5 = -5 -1i = -5 Divide each side by '-1'. i = 5 Simplifying i = 5Solution
i = {0.8, 5}
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