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

Let Z = + i = r(cosθ + isinθ)

Now , separating real and complex part , we get

= rcosθ ……….eq.1

1 = rsinθ …………eq.2

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

4 = r2

Since r is always a positive no., therefore,

r =2,

hence its modulus is 2.

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

Since , and . therefore the θ lies in first quadrant.

, therefore

Representing the complex no. in its polar form will be

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Write 2i in polar form.

RS Aggarwal - Mathematics