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Simplifying z = (1 + -5i)(1 + -1z) Multiply (1 + -5i) * (1 + -1z) z = (1(1 + -1z) + -5i * (1 + -1z)) z = ((1 * 1 + -1z * 1) + -5i * (1 + -1z)) z = ((1 + -1z) + -5i * (1 + -1z)) z = (1 + -1z + (1 * -5i + -1z * -5i)) z = (1 + -1z + (-5i + 5iz)) Reorder the terms: z = (1 + -5i + 5iz + -1z) z = (1 + -5i + 5iz + -1z) Solving z = 1 + -5i + 5iz + -1z 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 = 1 + -5i + 5iz + -5iz + -1z Combine like terms: 5iz + -5iz = 0 -5iz + z = 1 + -5i + 0 + -1z -5iz + z = 1 + -5i + -1z Add 'z' to each side of the equation. -5iz + z + z = 1 + -5i + -1z + z Combine like terms: z + z = 2z -5iz + 2z = 1 + -5i + -1z + z Combine like terms: -1z + z = 0 -5iz + 2z = 1 + -5i + 0 -5iz + 2z = 1 + -5i Reorder the terms: -1 + 5i + -5iz + 2z = 1 + -5i + -1 + 5i Reorder the terms: -1 + 5i + -5iz + 2z = 1 + -1 + -5i + 5i Combine like terms: 1 + -1 = 0 -1 + 5i + -5iz + 2z = 0 + -5i + 5i -1 + 5i + -5iz + 2z = -5i + 5i Combine like terms: -5i + 5i = 0 -1 + 5i + -5iz + 2z = 0 The solution to this equation could not be determined.
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