If so, then the Euler formula is much less aesthetic in my view... And, in IQ modulation, is the Q signal \$j\sin(\omega t)\$, or \$\sin(\omega t)\$?
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2no, it's not. basic math: wt is real, so sin(wt) is real, so j·sin(wt) is imaginary. sin(wt+90) is real, and since a non-zero imaginary number is not a real number, your title answers itself. – Marcus Müller Jul 01 '21 at 09:14
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also, this has nothing to do with optoelectronics, so I'm removing that tag :) – Marcus Müller Jul 01 '21 at 09:17
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1sin(wt+90) is cos(wt), or it might be -cos(wt), ICBA to think about the sign. – Neil_UK Jul 01 '21 at 09:26
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by the way, regarding your Q signal: it's neither. The Q signal is the result of mixing with a harmonic oscillation that's orthogonal to that used for the inphase branch. – Marcus Müller Jul 01 '21 at 09:32
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Thanks. This question was actually asking about the real meaning of the imaginary. Some people do interpret multiplying j as turning 90 degrees - not a reliable and comprehensive way of interpreting it, though. My understanding on this is that imaginary numbers are not simply turning the base real numbers by pi/2. We just picked the y-axis to represent imaginary numbers so as to construct a complex plane. It is not turning the vector on a real plane by pi/2. – Sherman Chen Jul 02 '21 at 00:41
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Yes, the Q signal should be cos(wt) which is the quadrature of the in-phase signal sin(wt). – Sherman Chen Jul 02 '21 at 00:50
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@MarcusMüller -- if $sin \left(\omega t\right) $ has an imaginary component, then $j sin \left(\omega t\right) $ has a real component ($j\times j$) – Scott Seidman Jul 14 '21 at 14:34
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Signals in electronics are real voltages and currents. If one wants to make something that acts like a mathematical, “complex signal”, one way of doing it is to use two channels, labeling one “real” and one “imaginary”. But, these are just labels. For example, one can create a signal, \$\exp(j\omega t)\$, by making a \$\cos(\omega t)\$ signal and labeling it “real”, and a \$\sin(\omega t)\$ signal (which of course is just a phase shifted \$\cos\$) , and labeling it “imaginary”. Doing the appropriate operations on the two channels can be equivalent to doing complex math on \$\exp(j\omega t)\$. Now our mathematics and our circuits are in correspondence!
