Answer:
The argument is 290.6°
Step-by-step explanation:
For a complex number:
Z = a + b*i
The argument is:
θ = Atan(b/a)
Where Atan(x) is the inverse function of the tangent function, such that:
Atan(tan(x)) = x
tan(Atan(x)) = x
In this case, we have the complex number:
Z = -3 + 8*i
The argument of this complex number will be:
θ = Atan(8/-3) = -69.4°
But we want 0°< θ <360⁰
Also, remember that the trigonometric functions have a periodicity of 360°
Then:
cos(θ + n*360°) = cos(θ)
With n integer.
This means that our angle is equivalent to:
-69.4° + 360° = 290.6°
Then the argument is 290.6°, this one is on the desired interval (0°, 360°)
