How to do a phasor calculation with radians using a principle of Eulers Formula

“How has this been calculated? I try to convert the 7.11 to radians and sum it up, then converting it back to degrees. However I do not get 1.61.”

-Quora question

My response:

The numbers are already in radians.

Dividing the coefficients does not seem to be the problem you had.

If you divide the e^x terms you would normally subtract the jπ/4 from the -j7.11.

That would get you

~-j7.8954

It’s best to save this in memory to not lose accuracy.

From there we can think about Euler’s formula. Shown on the right side in green. Much like the trigonometric functions we learn much before doing anything with phasors, you can add or subtract 2π to the input and get the same result for periodic functions. You can also do that with e^ix.

For this problem we add j2π to the -j7.8954 to get -j1.61. The answer is an approximation.