Question

the argument of √3 +i is​

Answer 1

Answer:

Correct option is

C

65π

Given, z=−3+i

We have ∣z∣=32+12=2

Therefore, cosθ=2−3

and sinθ=21

Hence, θ=65π

Answer 2

Given

The Argument of √(3) + i

Now

Where x = √(3) and y = 1

Its lie on 1st Quadrant  

Argument of Z

θ = Tan⁻¹(y/x)

θ = Tan⁻¹(1/√3)

θ = π/6

There are two type of type of Argument

i)principal Argument

Amp(z) = π/6

ii)General Value of Argument

Arg(z) = π/6 + 2kπ

More information

Properties of Argument

arg(Z₁.Z₂)=arg(Z₁)+arg(Z₂) + 2kπ

arg(Z₁/Z₂)= arg(Z₁)-arg(Z₂) + 2kπ

arg(Zⁿ)=n.arg(Z₂) + 2kπ