Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2.z = –1 – i√ 3

Given: z = –1 – i√ 3

Formulas:

Modulus of a complex number z = x + i y is given by,

|z| = √(x2 + y2)

So modulus of given z is,

|z| = √[(-1)2 + (√3)2]

|z| = √4 = 2

Now for argument let us find out the quadrant in which the complex number is present.
As real and imaginary parts are negative, z lies in third quadrant.

Thus Argument of z in third quadrant is,

arg(z) = α - π

And where,

α =  π/3

arg(z) = π/3 - π

= - 2π/3

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