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°)