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Let z=x+i y be a complex number where x ...

Let `z=x+i y` be a complex number where `x` and `y` are integers. Then, the area of the rectangle whose vertices are the roots of the equation `z z ^3+ z z^3=350` is 48 (b) 32 (c) 40 (d) 80

A

48

B

32

C

40

D

80

Text Solution

Verified by Experts

The correct Answer is:
A
`zbarz(barz^(2) + z^(2))= 350`
Putting z +iy, we have
`(x^(2) + y^(2)) (x^(2) -y^(2)) = 175`
`(x^(2) + y^(2)) (x^(2) -y^(2)) = 5 xx 5xx7`
`x^(2)+ y^(2) = 25`
`and x^(2) -y^(2) = 7`
(as other combinations given non-intergral values of x and y )
`therefore x = pm 4, y = pm 3 (x,y in I)`
Hence, area is `8 xx 6 = 48` sq . units
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