Students helping students, join us in improving Bored of Studies by donating and supporting future students!
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
becauseis not an inverse function of
.
Withit'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.