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1)

If   z=21+3i  repesents  a point P in the argand  plane and P lies in the third  quadrant , then the polar form of z is 


A) 2[cos(4π3)+isin(4π3)]

B) 2[cos(5π6)+isin(5π6)]

C) 2[cos(π6)+isin(π6)]

D) 2[cos(2π3)+isin(2π3)]

Answer:

Option B

Explanation:

We have

  z=21+3iz=2+23i

  z=(3+i)2z=±(3+i)

 z lie in third  quadrant

    z=3i

  |z|=(3)2+(1)2=3+1=4=2 and 

tanθ=|13|=13θ=π6

 Since   θ lie in 3rd quadrant

   arg(z)=(ππ6)=5π6

Hence,   z=2(cos(5π6)+isin(5π6))