Q. 185.0( 4 Votes )

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

Answer :

= 4i - 4

Let Z = 4i - 4 = r(cosθ + isinθ)

Now , separating real and complex part , we get

-4 = rcosθ ……….eq.1

= rsinθ …………eq.2

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

64 = r2

Since r is always a positive no., therefore,

r = 8,

hence its modulus is 8.

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

tanθ = -√3

Since , and tanθ = -√3. therefore the θ lies in second quadrant.

Tanθ = -√3, therefore

Representing the complex no. in its polar form will be


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