Q. 225.0( 2 Votes )

# Find the modulus of each of the following complex numbers and hence express each of them in polar form: (i25)3

Answer :

= i75

= i4n+3 where n = 18

since i4n+3 = -i

i75 = -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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RS Aggarwal - Mathematics