Convert each of the complex numbers given in Exercises 3 to 8 in the polar form : - 3

Solution:

The given complex number is,

z = -3 = r (cosθ + i sinθ) (Polar form) 

Let r cosθ = - 3 and r sinθ = 0

On squaring and adding, we obtain

r² cos² θ + r² sin² θ = (- 3)² + (0)²

⇒ r² (cos² θ + sin² θ) = 9

⇒ r² = 9

⇒ r = 3 [∵ Conventionally, r > 0]

Therefore,

3 cosθ = - 3 and 3 sinθ = 0

⇒ cosθ = - 1 and sinθ = 0

Since the θ lies in the quadrant II, θ = π

Hence,

- 3 = r cosθ + ir sinθ 

= 3cos π + i 3sin π

= 3(cos π + isin π)

Thus, this is the required polar form.

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NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.2 Question 6

Convert each of the complex numbers given in Exercises 3 to 8 in the polar form : - 3

Summary:

A complex number - 3 is given. We have found its polar form to be 3(cos π + isin π)