How do physicists use imaginary numbers?
An example: A force of 10 in the x direction and a force of 5 in the y direction will
produce what total force and at what angle? Force = x+iy = 10+5i. The total force will be (102+52).5 or (125).5 or 11.18. The angle will be atan y/x or atan 5/10 or .464 or 26.56 degrees.
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