Question

[
begin{array}{lr}
text { since, } & z bar{z}left(z^{2}+bar{z}^{2}right)=350
Rightarrow & 2left(x^{2}+y^{2}right)left(x^{2}-y^{2}right)=350
end{array}
]
( Rightarrow quadleft(x^{2}+y^{2}right)left(x^{2}-y^{2}right)=175 )
since, ( x, y in I, ) the only possible case which gives integral solution, is
[
begin{array}{l}
x^{2}+y^{2}=25
x^{2}-y^{2}=7
end{array}
]
From Eqs.
(i) and (ii),
[
x^{2}=16, y^{2}=9
]
( Rightarrow quad xi=pm 4, psi=pm 3 )
( therefore ) Area of rectangle ( =8 times 6=48 )

# of a Complex Number 5. 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 zzº + Z2 = 350, is (2009) (2) 48 (6) 32 (c) 40 (d) 80 TEL Z 1

Solution