Complex Numbers 2 Question 10

10. Let z=x+iy be a complex number where, x and y are integers. Then, the area of the rectangle whose vertices are the root of the equation zz¯3+z¯z3=350, is

(2009)

(a) 48

(b) 32

(c) 40

(d) 80

Show Answer

Answer:

Correct Answer: 10. (a)

Solution:

  1. Since,

zz¯(z2+z¯2)=350

2(x2+y2)(x2y2)=350

(x2+y2)(x2y2)=175

Since, x,yI, the only possible case which gives integral solution, is

x2+y2=25x2y2=7

From Eqs. (i) and (ii),

x2=16,y2=9x=±4,y=±3

Area of rectangle =8×6=48



NCERT Chapter Video Solution

Dual Pane