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I might have exaggerated a bit; there, the sine is also multiplied by i... Although it's still a combination :) But the fact that you can obtain perfectly real values for analysis by taking the real and imaginary parts of a complex number is a fact. Complex numbers do exist in one form or another, but they are simply difficult to imagine or measure. But the same is true for irrational numbers, and yet no one is afraid of the presence of a root or an exponent in equations.