# Worksheet: Modulus of a Complex Number

In this worksheet, we will practice using the general formula for calculating the modulus of a complex number.

Q1:

What is the modulus of the complex number ?

Q2:

What is the modulus of the complex number ?

• A3
• B10
• C
• D1
• E

Q3:

What is the modulus of the complex number ?

• A
• B
• C58
• D3
• E7

Q4:

What is the modulus of the complex number ?

Q5:

Given that , find .

• A
• B
• C
• D
• E

Q6:

Given that , find .

Q7:

Given that , find .

• A
• B
• C
• D
• E

Q8:

Given that , determine .

• A
• B
• C
• D

Q9:

If and , what is the modulus of ?

Q10:

Given that , determine .

Q11:

What is the modulus of the complex number , where and are real?

• A
• B
• C
• D
• E

Q12:

If , where is a complex number, what is ?

Q13:

Given that , where and , write in algebraic form and hence find .

• A,
• B,
• C,
• D,

Q14:

Given that , where and , write in algebraic form and hence find .

• A,
• B,
• C,
• D,

Q15:

Given the complex number , what is the modulus of ?

• A
• B
• C
• D
• E

Q16:

Given that , find .

• A
• B
• C
• D
• E

Q17:

Given that , where and are real numbers, determine the value of .

Q18:

Consider the complex numbers and . Given that and , which of the following is a possible value for ?

• A
• B
• C
• D
• E

Q19:

If and , what is ?

• A13
• B85
• C
• D145
• E

Q20:

What does the modulus of a complex number represent?

• Aits real coordinate in the complex plane
• Bthe angle it makes with the positive imaginary axis
• Cits imaginary coordinate in the complex plane
• Dthe angle it makes with the positive real axis
• Eits distance from the origin in the complex plane

Q21:

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

• A6
• B
• C3
• D

Q22:

What is given that ?

• A36
• B100
• C
• D6
• E

Q23:

Consider the complex numbers and .

Find and .

• A,
• B,
• C,
• D,
• E,

Calculate . How does this compare with ?

• A,
• B,
• C,
• D,
• E,

Calculate . How does this compare with ?

• A,
• B,
• C,
• D,
• E,

Q24:

Consider the two complex numbers and .

Calculate to two decimal places.

Calculate to two decimal places.

Which of the following relations do and satisfy?

• A
• B
• C
• D
• E

Q25:

If , where is a complex number, what is ?