Complex NumbersEasy
Question
Let z = x + iy be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation zz3 + zz3 = 350 is
Options
A.48
B.32
C.40
D.80
Solution
zz(z2 + z2) = 350
Put z = x + iy
(x2 + y2) (x2 - y2) = 175
(x2 + y2) (x2 - y2) = 5 . 5 . 7
x2 + y2 = 25
x2 - y2 = 7
x = ± 4, y = ± 3
x, y ∈ I
Area = 8 × 6 = 48 sq. unit.
Put z = x + iy
(x2 + y2) (x2 - y2) = 175
(x2 + y2) (x2 - y2) = 5 . 5 . 7
x2 + y2 = 25
x2 - y2 = 7
x = ± 4, y = ± 3
x, y ∈ I
Area = 8 × 6 = 48 sq. unit.
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