Answer:
390°
Step-by-step explanation:
The polar form of a complex number z=a+bi is z=r(cosθ+isinθ) .
So, we need to first find the absolute value of r .
r=|z|
Given: z = a + bi from the question √3+i
a =3 b=1
r = √a² + b² = √(√3)² + 1² = √3 + 1= √4 = 2
θ
=2π + tan⁻¹(b/
a
)
θ
=2π + tan⁻¹(1/√3
)
tan⁻¹(1/√3
)
= π
/6 or 30
°
θ = 2π + π/6 = 12π+π/6 = 13π/6 = 6.8 radians
converting it to degrees it 6.8 x 180/π = 389.611≈390°
