Q. 64.8( 4 Votes )

# Find the modulus of each of the following complex numbers and hence express each of them in polar form: –1 + i

Let Z = 1 - i = r(cosθ + isinθ)

Now , separating real and complex part , we get

-1 = rcosθ ……….eq.1

1 = rsinθ …………eq.2

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

2 = r2

Since r is always a positive no., therefore,

,

hence its modulus is √2.

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

Tanθ = -1

Since and tanθ = -1. therefore the θ lies in second quadrant.

Tanθ = -1, 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
RELATED QUESTIONS :

Write 2i in polar form.

RS Aggarwal - Mathematics