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Simplifying (4 + 7i)(-8 + 2i) = 0 Multiply (4 + 7i) * (-8 + 2i) (4(-8 + 2i) + 7i * (-8 + 2i)) = 0 ((-8 * 4 + 2i * 4) + 7i * (-8 + 2i)) = 0 ((-32 + 8i) + 7i * (-8 + 2i)) = 0 (-32 + 8i + (-8 * 7i + 2i * 7i)) = 0 (-32 + 8i + (-56i + 14i2)) = 0 Combine like terms: 8i + -56i = -48i (-32 + -48i + 14i2) = 0 Solving -32 + -48i + 14i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -24i + 7i2) = 0 Factor a trinomial. 2((-4 + -7i)(4 + -1i)) = 0 Ignore the factor 2.Subproblem 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 '(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 = 4Solution
i = {-0.5714285714, 4}
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