Question

Given that z=-1-i√3 , find the modulus and

the argument.​

Answer 1

z = -1 -i√3

Real part of z = -1

Imaginary part of z = -√3

In complex numbers,

argument = tan⁻¹ (imaginary part/real part)

here,

argument of z = tan⁻¹( -√3/-1) = tan⁻¹(√3) =  π/3 - π = -2π/3 [As  argument lies in 3rd quadrant]

argument of z = -2π/3

IzI (modulus) = √[(real part)² + (imaginary part)²]

IzI = √[(-3)² + (-1)²]

IzI = √(3+1) = 2

IzI = 2