Q. 73.9( 35 Votes )
Convert each of t
Let √3 = r cos θ and 1 = r sin θ ……….(i)
Squaring both sides, we get
3= r2 cos2 θ and 1 = r2 sin2 θ
Adding both the equations, we get
3 + 1 = r2 cos2 θ + r2 sin2 θ
⇒ 4 = r2 (cos2 θ + sin2 θ)
⇒ 4 = r2 or r2 = 4 [∵ sin2 θ + cos2 θ = 1]
⇒ r = √4
⇒ r = 2 (conventionally, r>0)
Substituting r = 2 in (i), we get
√3 = 2 cos θ and 1 = 2 sin θ
∵ We know that the complex number √3 + i lies in the first quadrant 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 .
Rate this question :
Write 2i in polarRS Aggarwal - Mathematics
Find the principaRS Aggarwal - Mathematics