Find the modulus and arguments of each of the complex numbers in Exercises 1 to 2:
z = - √3 + i

Solution:

The given complex number is,

z = - √3 + i

Let r cosθ = - √3 and r sinθ = 1

On squaring and adding, we obtain

r² cos² θ + r² sin² θ = (- √3)² + 1²

⇒ r² = 3 + 1 = 4 [∵ cos² θ+ sin² θ = 1]

⇒ r = √4 = 2 [∵ Conventionally, r > 0]

Therefore, Modulus = 2

Hence, 2 cosθ = - √3 and 2 sinθ = 1

⇒ cosθ = - √3/2 and sinθ = 1/2

Since θ lies in the quadrant II, θ = π - π/6 = 5π/6

Thus, the modulus and argument of the complex number - √3 + i are 2 and 5π/6 respectively.

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NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.2 Question 2

Find the modulus and arguments of each of the complex numbers in Exercises 1 to 2: z = - √3 + i

Summary:

A complex number is given. We have found that the modulus and argument of the complex number - √3 + i are 2 and 5π/6 respectively