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Because that is the way the tan function is defined!
No, white and tan are not the same colors. The links below show the difference between the colors.
The answer is relatively simple if you know hyperbolic functions. Suppose x is real so that ix is an imaginary number. Then tanh x = -i*tan(ix) So tan(ix) = (tanh x )/-i = i*tanh x = i * sinh x/csh x = i*(ex - e-x)/(ex + e-x) = i*(1 - e-2x)/(1 + e-2x)
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