Urgently need help!

Question

 

 

I dont understand what is after a), b), c) etc, what does it mean  {   }

Answer 1

(c)

Let z = x + iy

Now  plot the graph for (x+1)² +(y-1)² >1

 

So the answer is (E)

Answer 2

(a)

Let z = x + iy

Real part of z denotes as Re(z) = x

Imaginary part of z denotes as Im(z) = y

{ z : 1 ≤  Re(z)+Im(z)  < 2 }

Re(z)+Im(z) = x + y

Case 1: Let 1 ≤ x+y

Case 2: Let  x+y < 2

Now  plot the graph with above 2 cases

 

So option A is correct

Answer 3

(b)

Let z = x + iy

Real part of z denotes as Re(z) = x

Imaginary part of z denotes as Im(z) = y

{ z : 0 ≤ Im(z) < 1 }

Im(z) = y

Case 1: Let 0 ≤ y

Case 2: Let  y <1

Now  plot the graph with above 2 cases.

 

 

So the answer is (F)

Answer 4

(d)

Let z = x + iy

Case 1: Let  4 < [(x-1)² + (y-1)²]

Case 2: Let [ (x-1)² + (y-1)² ] ≤ 9

Now  plot the graph with above 2 cases.

 

So the answer is (B)

Answer 5

(e)

Let z = x + iy

Now  plot the graph for x² +(y+1)² ≤ 4

 

So the answer is (I)