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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