1
Question
If the roots of z3+iz2+2i=0 represents the vertices of a ΔABC in the Argand plane then the area of the triangle is
If the roots of z3+iz2+2i=0 represents the vertices of a ΔABC in the Argand plane then the area of the triangle is
Open in App
Solution
The correct option is D 2
One obvious root is i
Then
(z−i)(z2+2iz−2)=0
z=i
And
z2+2iz−2=0
(z+(i+1))(z+(i−1))=0
z=−i−1 and z=−i+1
Hence the triangle is formed by the vertices
A(0,1),B(−1,−1),C(1,−1)
Hence this is an isosceles triangle. with AB=AC
Considering BC as the base.
The vertical height will be given by the distance between A(0,1) and the midpoint of BC
Hence H=2
And Base=BC=2
Hence area
=B×H2
=2.
One obvious root is i
Then
(z−i)(z2+2iz−2)=0
z=i
And
z2+2iz−2=0
(z+(i+1))(z+(i−1))=0
z=−i−1 and z=−i+1
Hence the triangle is formed by the vertices
A(0,1),B(−1,−1),C(1,−1)
Hence this is an isosceles triangle. with AB=AC
Considering BC as the base.
The vertical height will be given by the distance between A(0,1) and the midpoint of BC
Hence H=2
And Base=BC=2
Hence area
=B×H2
=2.
Suggest Corrections
0
Similar questions