Question

if 90°<x<150° then argument of complex number z=1+cos2x+isin2x is​

Answer 1

Answer:

So the complex number z is given as

z=1−cos(2θ)−isin(2θ)z=1−cos(2θ)−isin(2θ)

And the question is to find the argument of z in terms of θθ.

So, I used the formula for calculating the argument of a complex number:

arg(z)=arctan(sin(2θ)1−cos(2θ))arg(z)=arctan(sin(2θ)1−cos(2θ))

=arctan(2sinθcosθ1−(1−2sin2θ))=arctan(2sinθcosθ1−(1−2sin2θ))

=arctan(2sinθcosθ2sin2θ)=arctan(2sinθcosθ2sin2θ)

=arctan(cosθsinθ)=arctan(cosθsinθ)

=arctan(cotθ)=arctan(cotθ)

=arctan(tan(π2−θ))=arctan(tan(π2−θ))

=π2−θ=π2−θ

But apparently the answer is θ−π2θ−π2. Where might have I gone wrong?

Edit: the domain given in the question for θθ was 0≤θ≤