What values of c and d would make the following expression represent a real number?i(2 + 3i)(c + di)

For the expression to be real, its imaginary part must be zero. Expanding gives i(2 + 3i)(c + di) = −(2d + 3c) + (2c − 3d)i, so we need 2c − 3d = 0. For c = −3 and d = −2, this is 2(−3) − 3(−2) = 0, so the expression is real.

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