Q. 145.0( 2 Votes )

Find the modulus of each of the following complex numbers and hence express each of them in polar form:

Answer :

= -i

Let Z = -i = r(cosθ + isinθ)

Now, separating real and complex part , we get

0 = rcosθ……….eq.1

-1 = rsinθ …………eq.2

Squaring and adding eq.1 and eq.2, we get

1 = r2

Since r is always a positive no., therefore,

r = 1,

hence its modulus is 1.

now, dividing eq.2 by eq.1 , we get,

Tanθ = -

Since cosθ = 0, sinθ = -1 and tanθ = -, therefore the θ lies in fourth quadrant.

Tanθ = -, therefore

Representing the complex no. in its polar form will be


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