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Simplifying z = (2 + 5i)(-4 + 2 + z) Combine like terms: -4 + 2 = -2 z = (2 + 5i)(-2 + z) Multiply (2 + 5i) * (-2 + z) z = (2(-2 + z) + 5i * (-2 + z)) z = ((-2 * 2 + z * 2) + 5i * (-2 + z)) z = ((-4 + 2z) + 5i * (-2 + z)) z = (-4 + 2z + (-2 * 5i + z * 5i)) z = (-4 + 2z + (-10i + 5iz)) Reorder the terms: z = (-4 + -10i + 5iz + 2z) z = (-4 + -10i + 5iz + 2z) Solving z = -4 + -10i + 5iz + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5iz' to each side of the equation. -5iz + z = -4 + -10i + 5iz + -5iz + 2z Combine like terms: 5iz + -5iz = 0 -5iz + z = -4 + -10i + 0 + 2z -5iz + z = -4 + -10i + 2z Add '-2z' to each side of the equation. -5iz + z + -2z = -4 + -10i + 2z + -2z Combine like terms: z + -2z = -1z -5iz + -1z = -4 + -10i + 2z + -2z Combine like terms: 2z + -2z = 0 -5iz + -1z = -4 + -10i + 0 -5iz + -1z = -4 + -10i Reorder the terms: 4 + 10i + -5iz + -1z = -4 + -10i + 4 + 10i Reorder the terms: 4 + 10i + -5iz + -1z = -4 + 4 + -10i + 10i Combine like terms: -4 + 4 = 0 4 + 10i + -5iz + -1z = 0 + -10i + 10i 4 + 10i + -5iz + -1z = -10i + 10i Combine like terms: -10i + 10i = 0 4 + 10i + -5iz + -1z = 0 The solution to this equation could not be determined.
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