Q. 213.8( 5 Votes )

Find the principal argument of (–2i).

Answer :

Let, z = -2i

Let 0 = rcosθ and -2 = rsinθ


By squaring and adding, we get


(0)2 + (-2)2 = (rcosθ)2 + (rsinθ)2


0+4 = r2(cos2θ + sin2θ)


4 = r2


r = 2


cosθ= 0 and sinθ=-1


Since, θ lies in fourth quadrant, we have



Since, θ (-π ,π ] it is principal argument.


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