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Simplifying (3 + 2i) * z + 5z = 4 Reorder the terms for easier multiplication: z(3 + 2i) + 5z = 4 (3 * z + 2i * z) + 5z = 4 Reorder the terms: (2iz + 3z) + 5z = 4 (2iz + 3z) + 5z = 4 Combine like terms: 3z + 5z = 8z 2iz + 8z = 4 Solving 2iz + 8z = 4 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-8z' to each side of the equation. 2iz + 8z + -8z = 4 + -8z Combine like terms: 8z + -8z = 0 2iz + 0 = 4 + -8z 2iz = 4 + -8z Divide each side by '2z'. i = 2z-1 + -4 Simplifying i = 2z-1 + -4 Reorder the terms: i = -4 + 2z-1
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