Q. 175.0( 2 Votes )
Find the modulus of each of the following complex numbers and hence express each of them in polar form: 
Answer :
= i + 1
Let Z = 1 + i = r(cosθ + isinθ)
Now , separating real and complex part , we get
1 = rcosθ ……….eq.1
1 = rsinθ …………eq.2
Squaring and adding eq.1 and eq.2, we get
2 = 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,
Tanθ = 1
Since 
, 
and tanθ = 1. therefore the θ lies in first quadrant.
Tanθ = 1, therefore
Representing the complex no. in its polar form will be
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