Q. 1

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

Answer :

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°)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Polar & Euler Form of Complex Numbers on Argand Plane32 mins
Interactive Quiz Time - Polar & Euler Form of complex number58 mins
Practice session | Argument of complex numbers61 mins
Modulus & Conjugate of Complex Number | Ready for a Quiz?48 mins
Interactive Quiz on Quadratic Equations73 mins
Special Quiz on Argument of complex numbers56 mins
Polar & Euler Form of Complex Number on Argand Plane58 mins
Questions on Modulus & Conjugate of Complex Number62 mins
Questions Based on Polar & Euler Form of Complex Number63 mins
Interactive Quiz on Quadratic Equations-0252 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses