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Simplifying z2 + -1(1 + I) * z + -2 + -1i = 0 Reorder the terms for easier multiplication: z2 + -1z(1 + I) + -2 + -1i = 0 z2 + (1 * -1z + I * -1z) + -2 + -1i = 0 z2 + (-1z + -1zI) + -2 + -1i = 0 Reorder the terms: -2 + -1i + -1z + -1zI + z2 = 0 Solving -2 + -1i + -1z + -1zI + 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 + -1i + -1z + -1zI + 2 + z2 = 0 + 2 Reorder the terms: -2 + 2 + -1i + -1z + -1zI + z2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1i + -1z + -1zI + z2 = 0 + 2 -1i + -1z + -1zI + z2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1i + -1z + -1zI + z2 = 2 Add 'z' to each side of the equation. -1i + -1z + -1zI + z + z2 = 2 + z Reorder the terms: -1i + -1z + z + -1zI + z2 = 2 + z Combine like terms: -1z + z = 0 -1i + 0 + -1zI + z2 = 2 + z -1i + -1zI + z2 = 2 + z Add 'zI' to each side of the equation. -1i + -1zI + zI + z2 = 2 + z + zI Combine like terms: -1zI + zI = 0 -1i + 0 + z2 = 2 + z + zI -1i + z2 = 2 + z + zI Add '-1z2' to each side of the equation. -1i + z2 + -1z2 = 2 + z + zI + -1z2 Combine like terms: z2 + -1z2 = 0 -1i + 0 = 2 + z + zI + -1z2 -1i = 2 + z + zI + -1z2 Divide each side by '-1'. i = -2 + -1z + -1zI + z2 Simplifying i = -2 + -1z + -1zI + z2
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