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Simplifying (-3 + 8i)(7 + 7i) = 0 Multiply (-3 + 8i) * (7 + 7i) (-3(7 + 7i) + 8i * (7 + 7i)) = 0 ((7 * -3 + 7i * -3) + 8i * (7 + 7i)) = 0 ((-21 + -21i) + 8i * (7 + 7i)) = 0 (-21 + -21i + (7 * 8i + 7i * 8i)) = 0 (-21 + -21i + (56i + 56i2)) = 0 Combine like terms: -21i + 56i = 35i (-21 + 35i + 56i2) = 0 Solving -21 + 35i + 56i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '7'. 7(-3 + 5i + 8i2) = 0 Factor a trinomial. 7((-1 + -1i)(3 + -8i)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-1 + -1i)' equal to zero and attempt to solve: Simplifying -1 + -1i = 0 Solving -1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1i = 0 + 1 -1i = 0 + 1 Combine like terms: 0 + 1 = 1 -1i = 1 Divide each side by '-1'. i = -1 Simplifying i = -1Subproblem 2
Set the factor '(3 + -8i)' equal to zero and attempt to solve: Simplifying 3 + -8i = 0 Solving 3 + -8i = 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 + -8i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8i = 0 + -3 -8i = 0 + -3 Combine like terms: 0 + -3 = -3 -8i = -3 Divide each side by '-8'. i = 0.375 Simplifying i = 0.375Solution
i = {-1, 0.375}
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