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

Given complex number is z=sin120⁰-icos120⁰

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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,

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⇒

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⇒ |z|=1

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

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⇒ .

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