Write 2i in polar form.
Let, z = 2i
Let 0 = rcosθ and 2 = rsinθ
By squaring and adding, we get
(0)2 + (2)2 = (rcosθ)2 + (rsinθ)2
⇒ 0+4 = r2(cos2θ + sin2θ)
⇒4 = r2
⇒ r = 2
∴ cosθ= 0 and sinθ=1
Since, θ lies in first quadrant, we have
Thus, the required polar form is