Write –3i in polar form.

1.	Write –3i in polar form.
Answer» Let, z = -3i Let 0 = r cosθ and -3 = r sinθ By squaring and adding, we get (0)²+ (-3)² = (r cosθ)² + (r sinθ)² ⇒ 0+9 = r²(cos²θ + sin²θ) ⇒ 9 = r² ⇒ r = 3 ∴ cosθ = 0 and sinθ = -1 Since, θ lies in fourth quadrant, we have θ = 3π/2 Thus, the required polar form is \(3[cos(3\frac{3\pi}{2})+i\,sin(\frac{3\pi}{2})]\)

Answer»

Let, z = -3i

Let 0 = r cosθ and -3 = r sinθ

By squaring and adding, we get

(0)²+ (-3)² = (r cosθ)² + (r sinθ)²

⇒ 0+9 = r²(cos²θ + sin²θ)

⇒ 9 = r²

⇒ r = 3

∴ cosθ = 0 and sinθ = -1

Since, θ lies in fourth quadrant, we have

θ = 3π/2

Thus, the required polar form is \(3[cos(3\frac{3\pi}{2})+i\,sin(\frac{3\pi}{2})]\)

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