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Simplifying z2 + (2i + 3) * z + (1 + 3i) = 0 Reorder the terms: z2 + (3 + 2i) * z + (1 + 3i) = 0 Reorder the terms for easier multiplication: z2 + z(3 + 2i) + (1 + 3i) = 0 z2 + (3 * z + 2i * z) + (1 + 3i) = 0 Reorder the terms: z2 + (2iz + 3z) + (1 + 3i) = 0 z2 + (2iz + 3z) + (1 + 3i) = 0 Remove parenthesis around (1 + 3i) z2 + 2iz + 3z + 1 + 3i = 0 Reorder the terms: 1 + 3i + 2iz + 3z + z2 = 0 Solving 1 + 3i + 2iz + 3z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 3i + 2iz + 3z + -1 + z2 = 0 + -1 Reorder the terms: 1 + -1 + 3i + 2iz + 3z + z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3i + 2iz + 3z + z2 = 0 + -1 3i + 2iz + 3z + z2 = 0 + -1 Combine like terms: 0 + -1 = -1 3i + 2iz + 3z + z2 = -1 Add '-3z' to each side of the equation. 3i + 2iz + 3z + -3z + z2 = -1 + -3z Combine like terms: 3z + -3z = 0 3i + 2iz + 0 + z2 = -1 + -3z 3i + 2iz + z2 = -1 + -3z Add '-1z2' to each side of the equation. 3i + 2iz + z2 + -1z2 = -1 + -3z + -1z2 Combine like terms: z2 + -1z2 = 0 3i + 2iz + 0 = -1 + -3z + -1z2 3i + 2iz = -1 + -3z + -1z2 Reorder the terms: 1 + 3i + 2iz + 3z + z2 = -1 + -3z + -1z2 + 1 + 3z + z2 Reorder the terms: 1 + 3i + 2iz + 3z + z2 = -1 + 1 + -3z + 3z + -1z2 + z2 Combine like terms: -1 + 1 = 0 1 + 3i + 2iz + 3z + z2 = 0 + -3z + 3z + -1z2 + z2 1 + 3i + 2iz + 3z + z2 = -3z + 3z + -1z2 + z2 Combine like terms: -3z + 3z = 0 1 + 3i + 2iz + 3z + z2 = 0 + -1z2 + z2 1 + 3i + 2iz + 3z + z2 = -1z2 + z2 Combine like terms: -1z2 + z2 = 0 1 + 3i + 2iz + 3z + z2 = 0 The solution to this equation could not be determined.
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