Question 8:

Convert the given complex number in polar form: i

Answer

i

Let r cosθ = 0 and r sin θ = 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]

∴ cos θ = 0 and sin θ = 1

∴ θ = π/2

This is the required polar form.

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