Write the complex number in polar form with argument ? between 0 and 2p. 7radical 3 - 7i

Question

Write the complex number in polar form with argument θ between 0 and 2π. 7radical 3 − 7i

Answer 1

Given a complex number z = 7√3 - 7i, let z= x + yi then x= 7√3, y = -7
writing in polar form z = r(cosθ + i sinθ)
where r = |z| = √(x2 + y2) = 14
θ = tan^-1(y/x) = tan^-1(-1/√3) = - π/6, or 11π/6, where 0≤θ≤2π, and π = pi

∴ z = 14(cos(11π/6) + i sin(11π/6))

Answer 2

See my other answer and consider  instead of 9 radical 3 / 9 you have 7 radical 3, making the magnitude 14 and theta pi/3.