Complex NumbersHard
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.
Create a free account to view solution
View Solution FreeMore Complex Numbers Questions
Mirror image of the curve = a, a ∈ R+ a ≠ 1 about the line |z - z1| = |z - z2| is given by...The centre of a square is at the origin and one of the vertex is 1 − i. The extremities of diagonal not passing th...The set of points on an Argand diagram which satisfy both |z| ≤ 4 & Arg z = is :...If z and ω are two non-zero complex numbers such that |zω| = 1, and Arg (z) - Arg(ω) = , then is equal to...If ( − 7 − 24i)1/2 = x − iy, then x2 + y2 is equal to-...