If $$z\left( {\overline {z + \alpha } } \right) + \overline z \left( {z + \alpha } \right) = 0,$$ where $$\alpha $$ is a complex constant, then $$z$$ is
represented by a point on
A.
a straight line
B.
a circle
C.
a parabola
D.
None of these
Answer :
a circle
Solution :
$$z\left( {\overline z + \overline \alpha } \right) + \overline z z + \alpha \overline z = 0$$
or, $$z\overline z + \frac{{\overline \alpha }}{2}z + \frac{\alpha }{2}\overline z = 0$$ which is a circle.
Releted MCQ Question on Algebra >> Complex Number
Releted Question 1
If the cube roots of unity are $$1,\omega ,{\omega ^2},$$ then the roots of the equation $${\left( {x - 1} \right)^3} + 8 = 0\,\,{\text{are}}$$