# Find the modulus of each of the following complex numbers and hence express each of them in polar form: 2 – 2i

Let Z = 2 - 2i = r(cosθ + isinθ)

Now , separating real and complex part , we get

2 = rcosθ ……….eq.1

-2 = rsinθ …………eq.2

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

8 = r2

Since r is always a positive no. therefore,

r = 2,

hence its modulus is 2√2.

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

Tanθ = -1

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

Tanθ = -1, therefore

Representing the complex no. in its polar form will be

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RELATED QUESTIONS :

Write 2i in polar form.

RS Aggarwal - Mathematics