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Simplifying z2 + (1 + -1i) * z + 2 = 0 Reorder the terms for easier multiplication: z2 + z(1 + -1i) + 2 = 0 z2 + (1 * z + -1i * z) + 2 = 0 Reorder the terms: z2 + (-1iz + 1z) + 2 = 0 z2 + (-1iz + 1z) + 2 = 0 Reorder the terms: 2 + -1iz + 1z + z2 = 0 Solving 2 + -1iz + 1z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -1iz + 1z + -2 + z2 = 0 + -2 Reorder the terms: 2 + -2 + -1iz + 1z + z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1iz + 1z + z2 = 0 + -2 -1iz + 1z + z2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1iz + 1z + z2 = -2 Add '-1z' to each side of the equation. -1iz + 1z + -1z + z2 = -2 + -1z Combine like terms: 1z + -1z = 0 -1iz + 0 + z2 = -2 + -1z -1iz + z2 = -2 + -1z Add '-1z2' to each side of the equation. -1iz + z2 + -1z2 = -2 + -1z + -1z2 Combine like terms: z2 + -1z2 = 0 -1iz + 0 = -2 + -1z + -1z2 -1iz = -2 + -1z + -1z2 Divide each side by '-1z'. i = 2z-1 + 1 + z Simplifying i = 2z-1 + 1 + z Reorder the terms: i = 1 + 2z-1 + z
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