Question

z1=1+3^(1÷2)​ i and z2=1+i then arg (z1/z2) is? ​

Answer 1

Answer:

∴ arg(Z₁/Z₂) = 15°

Step-by-step explanation:

Given,

Z₁ = 1+√3i

Here, x=1 and y=√3

r₁ = √(x²+y²) = √[(1)²+(√3)²] = 2

θ₁ = tan⁻¹(y/x) = tan⁻¹(√3/1) = 60°

In polar form,

Z₁ = 2(cos 60°+isin60°)

Z₂ = 1+i

Here, x=1 and y=1

r₂ = √(x²+y²) = √[(1)²+(1)²] = √2

θ₂ = tan⁻¹(y/x) = tan⁻¹(1/1) = 45°

In polar form,

Z₂ = √2(cos 45°+isin 45°)

Now,

arg(Z₁/Z₂) = arg(Z₁) - arg(Z₂)

                = θ₁-θ₂

                = 60°- 45°

                = 15°