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Simplifying (-7 + 4i)(1 + -8i) = 0 Multiply (-7 + 4i) * (1 + -8i) (-7(1 + -8i) + 4i * (1 + -8i)) = 0 ((1 * -7 + -8i * -7) + 4i * (1 + -8i)) = 0 ((-7 + 56i) + 4i * (1 + -8i)) = 0 (-7 + 56i + (1 * 4i + -8i * 4i)) = 0 (-7 + 56i + (4i + -32i2)) = 0 Combine like terms: 56i + 4i = 60i (-7 + 60i + -32i2) = 0 Solving -7 + 60i + -32i2 = 0 Solving for variable 'i'. Factor a trinomial. (-7 + 4i)(1 + -8i) = 0Subproblem 1
Set the factor '(-7 + 4i)' equal to zero and attempt to solve: Simplifying -7 + 4i = 0 Solving -7 + 4i = 0 Move all terms containing i to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 4i = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4i = 0 + 7 4i = 0 + 7 Combine like terms: 0 + 7 = 7 4i = 7 Divide each side by '4'. i = 1.75 Simplifying i = 1.75Subproblem 2
Set the factor '(1 + -8i)' equal to zero and attempt to solve: Simplifying 1 + -8i = 0 Solving 1 + -8i = 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 + -8i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8i = 0 + -1 -8i = 0 + -1 Combine like terms: 0 + -1 = -1 -8i = -1 Divide each side by '-8'. i = 0.125 Simplifying i = 0.125Solution
i = {1.75, 0.125}
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