Why not just add the two complex numbers as they are? This gives you z1 + z2 = 'something', and then just find the argument usingView attachment 27898
I turned z1 and z2 into modulus argument form so I got z1 = cos(pi/2)+isin(pi/2) and z2= cos(pi/4)+isin(pi/4) but I dont know how to prove arg(z1+z2) as I had never seen this identity before.
The argument of a complex number satisfiesWhy not just add the two complex numbers as they are? This gives you z1 + z2 = 'something', and then just find the argument using
Argument is calculated by taking tan inverse of the imaginary part over the real part of a complex number.
I waaas waiting for someone to say that imao.The argument of a complex number satisfies
This is not the same as
because is not an inverse function of .
With it's clear that the above does not hold, as the function can't possibly have an output of .
In the case of this question, both numbers have modulus 1. If you draw a diagram you can probably see that the argument of the sum will be the average of the sum of the arguments.
It's not negligible at all - it's the biggest defect in the "inverse" trig functions and it can completely throw off your calculations if you're not careful.It's such a small subtlety kinda negligible.