Question

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

Answer 1

Let Z = 2 - 2i = r(cosθ + i sinθ)

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√2,

Hence its modulus is 2√2.

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

Therefore the θ lies in the fourth quadrant.

Tanθ = -1, therefore θ = -π/4

Representing the complex no. in its polar form will be

Z = 2√2{cos(-π/4)+i sin(-π/4)}