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Simplifying (2 + -3i) * z + (2 + -3i) * z + -12 = 0 Reorder the terms for easier multiplication: z(2 + -3i) + (2 + -3i) * z + -12 = 0 (2 * z + -3i * z) + (2 + -3i) * z + -12 = 0 Reorder the terms: (-3iz + 2z) + (2 + -3i) * z + -12 = 0 (-3iz + 2z) + (2 + -3i) * z + -12 = 0 Reorder the terms for easier multiplication: -3iz + 2z + z(2 + -3i) + -12 = 0 -3iz + 2z + (2 * z + -3i * z) + -12 = 0 Reorder the terms: -3iz + 2z + (-3iz + 2z) + -12 = 0 -3iz + 2z + (-3iz + 2z) + -12 = 0 Reorder the terms: -12 + -3iz + -3iz + 2z + 2z = 0 Combine like terms: -3iz + -3iz = -6iz -12 + -6iz + 2z + 2z = 0 Combine like terms: 2z + 2z = 4z -12 + -6iz + 4z = 0 Solving -12 + -6iz + 4z = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '12' to each side of the equation. -12 + -6iz + 12 + 4z = 0 + 12 Reorder the terms: -12 + 12 + -6iz + 4z = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -6iz + 4z = 0 + 12 -6iz + 4z = 0 + 12 Combine like terms: 0 + 12 = 12 -6iz + 4z = 12 Add '-4z' to each side of the equation. -6iz + 4z + -4z = 12 + -4z Combine like terms: 4z + -4z = 0 -6iz + 0 = 12 + -4z -6iz = 12 + -4z Divide each side by '-6z'. i = -2z-1 + 0.6666666667 Simplifying i = -2z-1 + 0.6666666667 Reorder the terms: i = 0.6666666667 + -2z-1
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