# Worksheet: Regions in the Complex Plane

In this worksheet, we will practice using loci to identify regions in the complex plane.

**Q1: **

Which of the following represents the region of the complex plane defined by ?

- A(b)
- B(a)
- C(c)
- D(d)

**Q2: **

Which of the following systems of inequalities in terms of the complex number describes the region in an Argand diagram that is enclosed inside a rectangle of vertices , , , and and includes all the sides of the rectangle?

- A
- B
- C
- D
- E

**Q3: **

Which of the following represents the region of the complex plane defined by ?

- A(c)
- B(d)
- C(b)
- D(a)

**Q4: **

The shaded region in the following figure can be described as the intersection of two regions, each described by an inequality. Write both these inequalities in terms of .

- A,
- B,
- C,
- D,
- E,

**Q5: **

Which region satisfies the inequality ?

- A
- B
- C
- D
- E

**Q6: **

Which of the following shaded regions represents the locus of the point satisfying the system of inequalities , ?

- A(C)
- B(A)
- C(B)
- D(D)

**Q8: **

Which of the following represents the region of the complex plane defined by

- Ae
- Bd
- Cb
- Da
- Ec

**Q9: **

The shaded region in the following figure can be algebraically described by , where

Find the values of , , and , where and .

- A, ,
- B, ,
- C, ,
- D, ,
- E, ,

**Q10: **

We define the regions , , and in the complex plane as

Which of the following figures could represent the region of the complex plane defined by ?

- Aa
- Be
- Cc
- Db
- Ed

**Q11: **

The complex number satisfies the following conditions:

Which of the following shaded regions represents the locus of ?

- A
- B
- C
- D

Find the area of the locus of .

- A
- B
- C
- D

**Q12: **

Consider the following regions in the complex plane:

The region is defined as .

Which of the following shaded regions represents on an Argand diagram?

- A
- B
- C
- D

Find the area of the region .

- A
- B
- C
- D
- E

**Q13: **

On an Argand diagram, points and represent the complex numbers and respectively, where they are on the circles with centers and . represents the number and the number .

Describe the shaded region using **two** simultaneous inequalities which involve the modulus of complex numbers.

- A
- B
- C
- D
- E

Describe the shaded region using **one** double inequality which involves the argument of a complex number.

- A
- B
- C
- D
- E

**Q14: **

Which of the following shaded regions represents the locus of the point satisfying the inequality ?

- A(A)
- B(B)
- C(C)
- D(D)

**Q15: **

Which of the following shaded regions represents the region of the complex plane described by ?

- A(c)
- B(d)
- C(b)
- D(a)

**Q16: **

The complex number satisfies the following conditions:

- ,
- ,
- .

Represent the region on an Argand diagram.

- A
- B
- C
- D
- E

**Q17: **

On an Argand diagram, sketch the region represented by .

- A
- B
- C
- D
- E