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Simplifying (-4 + 9i)(4 + i) = 0 Multiply (-4 + 9i) * (4 + i) (-4(4 + i) + 9i * (4 + i)) = 0 ((4 * -4 + i * -4) + 9i * (4 + i)) = 0 ((-16 + -4i) + 9i * (4 + i)) = 0 (-16 + -4i + (4 * 9i + i * 9i)) = 0 (-16 + -4i + (36i + 9i2)) = 0 Combine like terms: -4i + 36i = 32i (-16 + 32i + 9i2) = 0 Solving -16 + 32i + 9i2 = 0 Solving for variable 'i'. Factor a trinomial. (-4 + -1i)(4 + -9i) = 0Subproblem 1
Set the factor '(-4 + -1i)' equal to zero and attempt to solve: Simplifying -4 + -1i = 0 Solving -4 + -1i = 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 + -1i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1i = 0 + 4 -1i = 0 + 4 Combine like terms: 0 + 4 = 4 -1i = 4 Divide each side by '-1'. i = -4 Simplifying i = -4Subproblem 2
Set the factor '(4 + -9i)' equal to zero and attempt to solve: Simplifying 4 + -9i = 0 Solving 4 + -9i = 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 + -9i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9i = 0 + -4 -9i = 0 + -4 Combine like terms: 0 + -4 = -4 -9i = -4 Divide each side by '-9'. i = 0.4444444444 Simplifying i = 0.4444444444Solution
i = {-4, 0.4444444444}
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