Q. 1

# Find the modulus of each of the following complex numbers and hence express each of them in polar form: 4

Let Z = 4 = r(cosθ + isinθ)

Now, separating real and complex part, we get

4 = rcosθ……….eq.1

0 = rsinθ…………eq.2

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

16 = r2

Since r is always a positive no., therefore,

r = 4,

hence its modulus is 4.

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

Tanθ = 0

Since cosθ = 1, sinθ = 0 and tanθ = 0. Therefore the θ lies in first quadrant.

Tanθ = 0, therefore θ = 0°

Representing the complex no. in its polar form will be

Z = 4(cos0° + isin0°)

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RS Aggarwal - Mathematics