Worksheet: Graphing Complex Numbers

Q1:

In which quadrant of the Argand diagram does the complex number lie?

• A second
• B third
• C first
• D fourth

Q2:

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

• A
• B
• C
• D

Q3:

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

• A
• B
• C
• D

Q4:

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

• A
• B
• C
• D

Q5:

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

• A
• B
• C
• D

Q6:

What does the modulus of a complex number represent?

• A the angle it makes with the positive imaginary axis
• B the angle it makes with the positive real axis
• C its real coordinate in the complex plane
• D its distance from the origin in the complex plane
• E its imaginary coordinate in the complex plane

Q7:

Given that the complex number is represented by the point on the Argand diagram below, find .

• A
• B
• C
• D
• E

Q8:

Given that the complex number is represented by the point on the Argand diagram below, find .

• A
• B
• C
• D
• E

Q9:

Given that the complex number is represented by the point on the Argand diagram below, find .

• A
• B
• C
• D
• E

Q10:

Given that the complex number is represented by the point on the Argand diagram below, find .

• A
• B
• C
• D
• E

Q11:

Given that , find .

• A
• B
• C
• D
• E

Q12:

Given that , find .

• A
• B
• C
• D
• E

Q13:

Given that , find .

• A
• B
• C
• D
• E

Q14:

Given that , determine the real part of the complex number .

• A6
• B3
• C
• D

Q15:

What complex number lies at the midpoint of and on the given complex plane?

• A
• B
• C
• D
• E

Q16:

The Argand diagram shows the complex numbers , , , and . Which of these numbers is ?

• A
• B
• C
• D

Q17:

Let us consider a complex number, , with nonzero real and imaginary parts.

If the real and imaginary parts of are of the same sign, in which quadrant(s) of the Argand diagram could appear?

• A1st or 2nd
• B2nd or 4th
• C3rd or 4th
• D1st or 3rd
• E1st or 4th

If the real and imaginary parts of are of opposite signs, in which quadrant(s) of the Argand diagram could appear?

• A2nd or 4th
• B3rd or 4th
• C1st or 2nd
• D1st or 3rd
• E1st or 4th