Q. 275.0( 2 Votes )

Match the statements of Column A and Column B.

Answer :

(a) Given z = i + √3


So, |z| = |i + √3|



= 2


Also, z lies in the first quadrant.



= π/6


The polar form of z is


(b) Given z = -1 + √-3


= -1 + i √3


Here z lies in the second quadrant.


arg (z) = amp (z)



= π – tan-1 √3


= π - π/3


= 2π/3


(c) Given |z + 2| = |z – 2|


|x + 2 + iy| = |x – 2 + iy|


(x + 2)2 + y2 = (x – 2)2 + y2


x2 + 4x + 4 = x2 – 4x + 4


8x = 0


x = 0


It is a straight line which is a perpendicular bisector of segment joining the points (-2, 0) and (2, 0).


(d) Given |z + 2i| = |z – 2i|


|x + i(y + 2)| = |x + i(y - 2)|


(x)2 + (y + 2)2 = (x)2 + (y – 2)2


4y = 0


y = 0


It is a straight line which is a perpendicular bisector of segment joining the points (0, -2) and (0, 2).


(e) Given |z + 4i| ≥ 3


|x + iy + 4i| ≤ 3


|x + i(y + 4)|≤ 3



(x)2 + (y + 4)2 ≤ 9


x2 + y2 + 8y + 16 ≤ 9


x2 + y2 + 8y + 7 ≤ 0


This represents the region on or outside circle having centre (0, -4) and radius 3.


(f) Given |z + 4| ≤ 3


|x + iy + 4| ≤ 3


|x + 4 + iy|≤ 3



(x + 4)2 + y2 ≤ 9


x2 + 8x + 16 + y2 ≤ 9


x2 + 8x + y2 + 7 ≤ 0


This represents the region on or inside circle having centre (-4, 0) and radius 3.


(g) Given






Hence z̅ lies in the third quadrant.


(h) Given z̅ = 1 - i


lies in the third quadrant.


,outr inside circle having centre (-4, 0) and radius 3.nts (-2, x numbers is not possible or has no



= 1/2 (1 + i)


Reciprocal of z lies in first quadrant.


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 PlanePolar & Euler Form of Complex Numbers on Argand PlanePolar & Euler Form of Complex Numbers on Argand Plane32 mins
Interactive Quiz Time - Polar & Euler Form of complex numberInteractive Quiz Time - Polar & Euler Form of complex numberInteractive Quiz Time - Polar & Euler Form of complex number58 mins
Practice session | Argument of complex numbersPractice session | Argument of complex numbersPractice session | Argument of complex numbers61 mins
Modulus & Conjugate of Complex Number | Ready for a Quiz?Modulus & Conjugate of Complex Number | Ready for a Quiz?Modulus & Conjugate of Complex Number | Ready for a Quiz?48 mins
Interactive Quiz on Quadratic EquationsInteractive Quiz on Quadratic EquationsInteractive Quiz on Quadratic Equations73 mins
Questions on Modulus & Conjugate of Complex NumberQuestions on Modulus & Conjugate of Complex NumberQuestions on Modulus & Conjugate of Complex Number62 mins
Special Quiz on Argument of complex numbersSpecial Quiz on Argument of complex numbersSpecial Quiz on Argument of complex numbers56 mins
Polar & Euler Form of Complex Number on Argand PlanePolar & Euler Form of Complex Number on Argand PlanePolar & Euler Form of Complex Number on Argand Plane58 mins
Questions Based on Polar & Euler Form of Complex NumberQuestions Based on Polar & Euler Form of Complex NumberQuestions Based on Polar & Euler Form of Complex Number63 mins
Interactive Quiz on Quadratic Equations-02Interactive Quiz on Quadratic Equations-02Interactive 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
caricature
view all courses