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To calculate the cotangent of a complex number, use the formula cot(z) = cos(z)/sin(z).

To use this formula, first find the cosine and sine of the complex number. For example, let's find the cotangent of z = 2 + 3i.

cos(z) = cos(2 + 3i) = cos(2)cosh(3) - sin(2)sinh(3) ≈ -3.724

sin(z) = sin(2 + 3i) = sin(2)cosh(3) + cos(2)sinh(3) ≈ 1.249

Then, plug these values into the formula:

cot(z) = cos(z)/sin(z) ≈ -2.981

Therefore, the cotangent of z = 2 + 3i is approximately -2.981.

Note that the cotangent of a complex number is a complex number itself, so it has both a real and imaginary part. In this example, the real part is negative and the imaginary part is zero.

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