Complex Number MCQ Level - 2 - IIT JAM MCQ

⇒ y + x = - 1 ,x > - 4 , y < 3 ...(2)
so, there is no point of intersection.
The correct answer is: None of these

( x - 1 ) ( x - α₁) ( x - α2) ...( x - α₈) ≡ x⁹ - 1
∴ ( 2 - α₁ )  ( 2 - α₂ )... ( 2 - α₈ ) = 2⁹ - 1
Now since  2 - α₁ and 2 - α₈ ) are conjugates of each other

similarly

and


The correct answer is: 

or

Let us write z as x+iy
We then have ∣2z−1∣=∣z−1∣
⇒4x²−8x+1+4y²=x²−2x+1+y²
⇒3x²+3y²−6x=0 which is a circle.
So, locus of z is a circle.

|t| = 1

The correct answer is: circle

T he correct answer is: -128 ω²

Point B has least principal argument


The correct answer is: 

Equation of the line is 2x - 2y = 0
i.e. y = x


The correct answer is : 

See the figure

 |z - 5i| < 3
the point is ( 4 cosθ, 4 sinθ)

The correct answer is: 

Let 

Since ‘r ’ cannot be zero

which will hold for
 and 5 distinct value o f 'O'
Thus there are five solution.
The correct answer is: 5