Find the modulus and argument of the following complex numbers and hence express each of them in the polar form :

Question

Find the modulus and argument of the following complex numbers and hence express each of them in the polar form : sin 120 o – i cos 120 o

Philoid · Accepted Answer

Given complex number is z=sin120⁰-icos120⁰

⇒

We know that the polar form of a complex number Z=x+iy is given by Z=|Z|(cosθ+isinθ)

Where,

|Z|=modulus of complex number=

θ =arg(z)=argument of complex number=

Now for the given problem,

⇒

⇒ |z|=1

⇒

Since x>0,y>0 complex number lies in 1^st quadrant and the value of θ will be as follows 0⁰≤θ≤90⁰.

⇒

⇒ .

⇒

∴ The Polar form of Z=sin120⁰-icos120⁰ is .