Q. 84.1( 27 Votes )
Convert each of t
Let 0 = r cos θ and 1 = r sin θ……….(i)
Squaring both sides, we get
0= r2 cos2 θ and 1 = r2 sin2 θ
Adding both the equations, we get
0 + 1 = r2 cos2 θ + r2 sin2 θ
⇒ 1 = r2 (cos2 θ + sin2 θ)
⇒ 1 = r2 or r2 = 1 [∵ sin2 θ + cos2 θ = 1]
⇒ r = √1
⇒ r = 1 (conventionally, r>0)
Substituting r = √2 in (i), we get
0 = cos θ and 1 = sin θ
⇒ cos θ = 0 and sin θ = 1
⇒ θ = cos-1 0 and θ = sin-1 1
∵ We know that the complex number i lies on the imaginary axis (y-axis) and the value of the argument lies between - π and π, i.e. - π < θ ≤ π.
As we know that the polar representation of a complex number z = x + iy is
z = r (cos θ + i sin θ) where is the modulus of the complex number and θ is the argument of the complex number, denoted by arg z.
So, the required polar form is .
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