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

Let Z = - + 1 = r(cosθ + isinθ)

Now , separating real and complex part , we get

1 = rcosθ ……….eq.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 the fourth quadrant.

Tanθ = , therefore θ =

Representing the complex no. in its polar form will be

Z = 2{cos + isin}

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Write 2i in polar form.

RS Aggarwal - Mathematics