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Simplifying (-5 + 3i)(4 + 7i) = 0 Multiply (-5 + 3i) * (4 + 7i) (-5(4 + 7i) + 3i * (4 + 7i)) = 0 ((4 * -5 + 7i * -5) + 3i * (4 + 7i)) = 0 ((-20 + -35i) + 3i * (4 + 7i)) = 0 (-20 + -35i + (4 * 3i + 7i * 3i)) = 0 (-20 + -35i + (12i + 21i2)) = 0 Combine like terms: -35i + 12i = -23i (-20 + -23i + 21i2) = 0 Solving -20 + -23i + 21i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + -7i)(5 + -3i) = 0Subproblem 1
Set the factor '(-4 + -7i)' equal to zero and attempt to solve: Simplifying -4 + -7i = 0 Solving -4 + -7i = 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 + -7i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7i = 0 + 4 -7i = 0 + 4 Combine like terms: 0 + 4 = 4 -7i = 4 Divide each side by '-7'. i = -0.5714285714 Simplifying i = -0.5714285714Subproblem 2
Set the factor '(5 + -3i)' equal to zero and attempt to solve: Simplifying 5 + -3i = 0 Solving 5 + -3i = 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 + -3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3i = 0 + -5 -3i = 0 + -5 Combine like terms: 0 + -5 = -5 -3i = -5 Divide each side by '-3'. i = 1.666666667 Simplifying i = 1.666666667Solution
i = {-0.5714285714, 1.666666667}
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