Trigonometric Form of a Complex Number...2

Section 6.6

 

4+4sqrt(3)*i

Use
z=a+bi=|z|(cos(θ)+i*sin(θ))
|z|=8
θ = arctan(b / a)
θ = arctan(4sqrt(3) / 4)
θ = arctan(sqrt(3) )
θ = π/3

|z|(cos(θ)+i*sin(θ)) =8(cos(π/3)+i*sin(π/3))

 

You said:

4 + 4sqrt(3)*i

Question 8 is 4 - 4sqrt(3)*i.

 

You said to use θ = arctan(b / a).

Section 6.6 tells me to use θ = 2pi + arctan(b / a).

Which is it?