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

Let

Now, separating real and complex part , we get

……….eq.1

…………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 = 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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RS Aggarwal - Mathematics