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Simplifying [x + -1(8 + -4i)][x + (8 + 4i)] = 0 [x + (8 * -1 + -4i * -1)][x + (8 + 4i)] = 0 [x + (-8 + 4i)][x + (8 + 4i)] = 0 Reorder the terms: [-8 + 4i + x][x + (8 + 4i)] = 0 Remove parenthesis around (8 + 4i) [-8 + 4i + x][x + 8 + 4i] = 0 Reorder the terms: [-8 + 4i + x][8 + 4i + x] = 0 Multiply [-8 + 4i + x] * [8 + 4i + x] [-8[8 + 4i + x] + 4i * [8 + 4i + x] + x[8 + 4i + x]] = 0 [[8 * -8 + 4i * -8 + x * -8] + 4i * [8 + 4i + x] + x[8 + 4i + x]] = 0 [[-64 + -32i + -8x] + 4i * [8 + 4i + x] + x[8 + 4i + x]] = 0 [-64 + -32i + -8x + [8 * 4i + 4i * 4i + x * 4i] + x[8 + 4i + x]] = 0 Reorder the terms: [-64 + -32i + -8x + [32i + 4ix + 16i2] + x[8 + 4i + x]] = 0 [-64 + -32i + -8x + [32i + 4ix + 16i2] + x[8 + 4i + x]] = 0 [-64 + -32i + -8x + 32i + 4ix + 16i2 + [8 * x + 4i * x + x * x]] = 0 Reorder the terms: [-64 + -32i + -8x + 32i + 4ix + 16i2 + [4ix + 8x + x2]] = 0 [-64 + -32i + -8x + 32i + 4ix + 16i2 + [4ix + 8x + x2]] = 0 Reorder the terms: [-64 + -32i + 32i + 4ix + 4ix + 16i2 + -8x + 8x + x2] = 0 Combine like terms: -32i + 32i = 0 [-64 + 0 + 4ix + 4ix + 16i2 + -8x + 8x + x2] = 0 [-64 + 4ix + 4ix + 16i2 + -8x + 8x + x2] = 0 Combine like terms: 4ix + 4ix = 8ix [-64 + 8ix + 16i2 + -8x + 8x + x2] = 0 Combine like terms: -8x + 8x = 0 [-64 + 8ix + 16i2 + 0 + x2] = 0 [-64 + 8ix + 16i2 + x2] = 0 Solving -64 + 8ix + 16i2 + x2 = 0 Solving for variable 'i'. The solution to this equation could not be determined.
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