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Simplifying z2 + -1(5 + 2i) + z + 21 + i = 0 z2 + (5 * -1 + 2i * -1) + z + 21 + i = 0 z2 + (-5 + -2i) + z + 21 + i = 0 Reorder the terms: -5 + 21 + -2i + i + z + z2 = 0 Combine like terms: -5 + 21 = 16 16 + -2i + i + z + z2 = 0 Combine like terms: -2i + i = -1i 16 + -1i + z + z2 = 0 Solving 16 + -1i + z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -1i + z + -16 + z2 = 0 + -16 Reorder the terms: 16 + -16 + -1i + z + z2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1i + z + z2 = 0 + -16 -1i + z + z2 = 0 + -16 Combine like terms: 0 + -16 = -16 -1i + z + z2 = -16 Add '-1z' to each side of the equation. -1i + z + -1z + z2 = -16 + -1z Combine like terms: z + -1z = 0 -1i + 0 + z2 = -16 + -1z -1i + z2 = -16 + -1z Add '-1z2' to each side of the equation. -1i + z2 + -1z2 = -16 + -1z + -1z2 Combine like terms: z2 + -1z2 = 0 -1i + 0 = -16 + -1z + -1z2 -1i = -16 + -1z + -1z2 Divide each side by '-1'. i = 16 + z + z2 Simplifying i = 16 + z + z2
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