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Simplifying z = (5 + -5i)(3 + 2i + z) Multiply (5 + -5i) * (3 + 2i + z) z = (5(3 + 2i + z) + -5i * (3 + 2i + z)) z = ((3 * 5 + 2i * 5 + z * 5) + -5i * (3 + 2i + z)) z = ((15 + 10i + 5z) + -5i * (3 + 2i + z)) z = (15 + 10i + 5z + (3 * -5i + 2i * -5i + z * -5i)) Reorder the terms: z = (15 + 10i + 5z + (-15i + -5iz + -10i2)) z = (15 + 10i + 5z + (-15i + -5iz + -10i2)) Reorder the terms: z = (15 + 10i + -15i + -5iz + -10i2 + 5z) Combine like terms: 10i + -15i = -5i z = (15 + -5i + -5iz + -10i2 + 5z) Solving z = 15 + -5i + -5iz + -10i2 + 5z 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 = 15 + -5i + -5iz + -10i2 + 5iz + 5z Reorder the terms: 5iz + z = 15 + -5i + -5iz + 5iz + -10i2 + 5z Combine like terms: -5iz + 5iz = 0 5iz + z = 15 + -5i + 0 + -10i2 + 5z 5iz + z = 15 + -5i + -10i2 + 5z Add '-5z' to each side of the equation. 5iz + z + -5z = 15 + -5i + -10i2 + 5z + -5z Combine like terms: z + -5z = -4z 5iz + -4z = 15 + -5i + -10i2 + 5z + -5z Combine like terms: 5z + -5z = 0 5iz + -4z = 15 + -5i + -10i2 + 0 5iz + -4z = 15 + -5i + -10i2 Reorder the terms: -15 + 5i + 5iz + 10i2 + -4z = 15 + -5i + -10i2 + -15 + 5i + 10i2 Reorder the terms: -15 + 5i + 5iz + 10i2 + -4z = 15 + -15 + -5i + 5i + -10i2 + 10i2 Combine like terms: 15 + -15 = 0 -15 + 5i + 5iz + 10i2 + -4z = 0 + -5i + 5i + -10i2 + 10i2 -15 + 5i + 5iz + 10i2 + -4z = -5i + 5i + -10i2 + 10i2 Combine like terms: -5i + 5i = 0 -15 + 5i + 5iz + 10i2 + -4z = 0 + -10i2 + 10i2 -15 + 5i + 5iz + 10i2 + -4z = -10i2 + 10i2 Combine like terms: -10i2 + 10i2 = 0 -15 + 5i + 5iz + 10i2 + -4z = 0 The solution to this equation could not be determined.
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