# Lesson Worksheet: Argand Diagram Mathematics • 12th Grade

In this worksheet, we will practice identifying complex numbers plotted on an Argand diagram and discovering their geometric properties.

Q1:

If the number is represented on Argand diagram by the point , determine the Cartesian coordinates of that point.

• A
• B
• C
• D

Q2:

Seven complex numbers , , , , , , and are represented on the Argand diagram. Which of the complex numbers is ?

• A
• B
• C
• D
• E

What complex number is represented by ?

• A
• B
• C
• D
• E

Which complex number has equal real and imaginary parts?

• A
• B
• C
• D
• E

Which two complex numbers are a conjugate pair? What is their geometric relationship?

• A and are a conjugate pair; they are related by a rotation about the origin of radians.
• B and are a conjugate pair; they are related by reflection in the real axis (-axis).
• CNone of the complex numbers are a conjugate pair.
• D and are a conjugate pair; they are related by reflection in the imaginary axis (-axis).
• E and are a conjugate pair; they are related by reflection in the real axis (-axis).

Q3:

What complex number lies at the midpoint of and on the given complex plane? • A
• B
• C
• D
• E

Q4:

Using the Argand diagram shown, find the value of . • A
• B
• C
• D
• E

Q5:

Using the Argand diagram shown, find the value of . Q6:

Three complex numbers, , , and , are represented on the Argand diagram. Find the complex number that lies at the midpoint between and .

• A
• B
• C
• D
• E

Find the value of .

• A
• B
• C
• D
• E

Q7:

What is the geometric relationship between the points representing a conjugate pair of complex numbers on an Argand diagram?

• AThey both lie on the imaginary axis.
• BThey are reflections of each other in the real axis.
• CThey are rotations of each other of radians counterclockwise about the origin.
• DThey both lie on the real axis.
• EThey are reflections of each other in the imaginary axis.

Q8:

Using the Argand diagram below, find the value of . • A
• B
• C
• D
• E

Q9:

Consider the complex number . If is represented on an Argand diagram by the point , in which quadrant of the Argand plane does lie?

• AFirst
• BSecond
• CThird
• DFourth

Q10:

Find the value of given on the Argand diagram below. • A
• B
• C
• D
• E