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Simplifying (3 + 5i)(-4 + 7i) = 0 Multiply (3 + 5i) * (-4 + 7i) (3(-4 + 7i) + 5i * (-4 + 7i)) = 0 ((-4 * 3 + 7i * 3) + 5i * (-4 + 7i)) = 0 ((-12 + 21i) + 5i * (-4 + 7i)) = 0 (-12 + 21i + (-4 * 5i + 7i * 5i)) = 0 (-12 + 21i + (-20i + 35i2)) = 0 Combine like terms: 21i + -20i = 1i (-12 + 1i + 35i2) = 0 Solving -12 + 1i + 35i2 = 0 Solving for variable 'i'. Factor a trinomial. (-3 + -5i)(4 + -7i) = 0Subproblem 1
Set the factor '(-3 + -5i)' equal to zero and attempt to solve: Simplifying -3 + -5i = 0 Solving -3 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -5i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5i = 0 + 3 -5i = 0 + 3 Combine like terms: 0 + 3 = 3 -5i = 3 Divide each side by '-5'. i = -0.6 Simplifying i = -0.6Subproblem 2
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 = 0.5714285714Solution
i = {-0.6, 0.5714285714}
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