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Write the real straight line y = m*x + c (m, c real) in complex-number form, using z = x + i*y and z-bar for its conjugate.

1. m(z + z-bar) + 2c - i(z - z-bar) = 0
2. m(z + z-bar) + 2c + i(z - z-bar) = 0
3. m(z + z-bar) - 2c + i(z - z-bar) = 0
4. m(z - z-bar) - 2c + i(z + z-bar) = 0

Correct answer: m(z + z-bar) + 2c - i(z - z-bar) = 0

Solution

Substituting x and y in terms of z and z-bar into y = m*x + c and simplifying gives m(z + z-bar) + 2c - i(z - z-bar) = 0.

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