# 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)

Q7:

The figure shows a region in the complex plane. Write an algebraic description of the shaded region.

• A
• B
• C
• D
• E

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:

1. ,
2. ,
3. .

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 