Q. 215.0( 3 Votes )
Find the modulus of each of the following complex numbers and hence express each of them in polar form: 
Answer :
Let Z = -
- √3 = r(cosθ + isinθ)
Now , separating real and complex part , we get
-√3 = rcosθ ……….eq.1
-1 = rsinθ …………eq.2
Squaring and adding eq.1 and eq.2, we get
4 = r2
Since r is always a positive no., therefore,
r = 2
hence its modulus is 2.
now, dividing eq.2 by eq.1, we get,
Since 
, 
and 
. therefore the θ lies in third quadrant.
, therefore 
.
Representing the complex no. in its polar form will be
}
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