of a Complex Number 5. Let z = x+iy...
Question

# 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

JEE/Engineering Exams
Maths
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[ 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 )