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Simplifying z2 + -1(3 + i) * z + 4 = 0 Reorder the terms for easier multiplication: z2 + -1z(3 + i) + 4 = 0 z2 + (3 * -1z + i * -1z) + 4 = 0 Reorder the terms: z2 + (-1iz + -3z) + 4 = 0 z2 + (-1iz + -3z) + 4 = 0 Reorder the terms: 4 + -1iz + -3z + z2 = 0 Solving 4 + -1iz + -3z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -1iz + -3z + -4 + z2 = 0 + -4 Reorder the terms: 4 + -4 + -1iz + -3z + z2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1iz + -3z + z2 = 0 + -4 -1iz + -3z + z2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1iz + -3z + z2 = -4 Add '3z' to each side of the equation. -1iz + -3z + 3z + z2 = -4 + 3z Combine like terms: -3z + 3z = 0 -1iz + 0 + z2 = -4 + 3z -1iz + z2 = -4 + 3z Add '-1z2' to each side of the equation. -1iz + z2 + -1z2 = -4 + 3z + -1z2 Combine like terms: z2 + -1z2 = 0 -1iz + 0 = -4 + 3z + -1z2 -1iz = -4 + 3z + -1z2 Divide each side by '-1z'. i = 4z-1 + -3 + z Simplifying i = 4z-1 + -3 + z Reorder the terms: i = -3 + 4z-1 + z
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