# Worksheet: Argand Diagrams

Q1:

Consider the complex number .

Find the modulus of .

• A1
• B3
• C
• D
• E

Hence, find the modulus of .

• A
• B10
• C
• D243
• E

Q2:

Find the complex number such that lies at the midpoint of and when they are represented on a complex plane.

• A
• B
• C
• D
• E

Q3:

Given that , find the principal argument of rounded to the nearest two decimal places.

Q4:

Find the possible real values of such that the distance between the complex number and the complex number is 5.

• A 5 or 9
• B 5
• C 1.7 or 15.7
• D 3 or 11
• E 0.5 or 14.5

Q5:

Given that , find the principal argument of rounded to the nearest two decimal places.

Q6:

Given that , find the principal argument of rounded to the nearest two decimal places.

Q7:

Given that , find the principal argument of rounded to the nearest two decimal places.

Q8:

Given that , find the principal argument of .

• A
• B
• C0
• D

Q9:

Given that , find the principal argument of .

• A
• B
• C
• D

Q10:

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

Q11:

What complex number lies at the midpoint of the complex numbers and , where , , , and are real, when they are represented on a complex plane?

• A
• B
• C
• D
• E

Q12:

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

• A6
• B3
• C
• D

Q13:

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

Q14:

• A
• B
• C
• D

Q15:

If , find .

• A
• B
• C
• D
• E