Hi and thank you in advance. I understand that one of Euler's formulas states:
cos(x) + isin(x) = e^ix
I know that if you were to have the same coefficient attached to sin and cos the following would hold true:
4*cos(x) + 4*isin(x) = 4*e^ix or z*cos(x) + z*isin(x) = z*e^ix
Additionally a constant could be applied inside the trig term and this would hold true:
cos(3x) + isin(3x) = e^3ix or cos(xt) + isin(xt) = e^ixt
I have trouble understanding how we can utilize this though say if any of the above coefficients were to not be uniform. Say:
4*cos(x) + 3*isin(x) = ?
If you were to say the above is equivalent to 7e^ix, this not true. How can you use eulers formula with different coefficients? Is it possible?
and somehow through Euler's converted it to the following: