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

Solution:

The given complex number is,

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

Let r cosθ = 0 and r sinθ = 1

On squaring and adding, we obtain

r² cos² θ + r² sin² θ = 0² + 1²

⇒ r² (cos² θ + sin² θ) = 1

⇒ r² = 1

⇒ r = √1 = 1 [∵ Conventionally, r > 0]

Therefore, cosθ = 0 and sinθ = 1

Since, θ lies in quadrant I, θ = π/2

Hence,

i = r cosθ + ir sinθ

= cos π/2 + i sin π/2

Thus, this is the required polar form

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NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.2 Question 8

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

Summary:

A complex number i is given. We have found its polar form to be i = cos π/2 + i sin π/2