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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. (-5 + i)(4 + -5i) = 0Subproblem 1
Set the factor '(-5 + i)' equal to zero and attempt to solve: Simplifying -5 + i = 0 Solving -5 + i = 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 + i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + i = 0 + 5 i = 0 + 5 Combine like terms: 0 + 5 = 5 i = 5 Simplifying i = 5Subproblem 2
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 = 0.8Solution
i = {5, 0.8}
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