# Lesson Worksheet: Introduction to Complex Numbers Mathematics

In this worksheet, we will practice dealing with imaginary numbers, knowing that complex numbers are made of a real part and an imaginary part.

Q1:

True or False: Any complex number is also a real number.

• AFalse
• BTrue

Q2:

If , what is ?

Q3:

If , what is ?

Q4:

True or False: Any imaginary number is also a complex number.

• AFalse
• BTrue

Q5:

What type of number is ?

• Areal
• Bcomplex
• Cpurely imaginary

Q6:

What is the real part of the complex number ?

Q7:

What is the imaginary part of the complex number ?

Q8:

If is a real number, what is the value of ?

Q9:

If is an imaginary number, what is the value of ?

Q10:

If , which of the following statements is correct?

• A,
• B,
• C,
• D,
• E,

Q11:

• A
• B
• C
• D
• E

Q12:

True or False: Any real number is also a complex number.

• ATrue
• BFalse

Q13:

Express in terms of .

• A
• B
• C
• D
• E

Q14:

The complex numbers are a field in part because .

• A is a real vector space
• Bfor every non-zero there is a such that
• C for all
• D

Q15:

Find the value of .

• A
• B
• C12
• D
• E

Q16:

What is ?

• A
• B
• C
• D
• E5

Q17:

What type of number is ?

• AReal
• BPure imaginary
• CComplex

Q18:

Which of the following defines ?

• AIt is the number whose square equals 1.
• BIt is the number whose square equals .
• CIt is the number whose square equals .
• DIt is the number whose square equals 2.

Q19:

Solve the following equation: .

• A
• B
• C
• D
• E

Q20:

True or False: The solution of the equation exists in the set of real numbers .

• ATrue
• BFalse

Q21:

What is the value of ?

Q22:

What is the value of ?

Q23:

What is the value of ?

• A8
• B
• C
• D
• E

Q24:

Complete the following: If the two complex numbers and are equal, then and .

• A3, 2
• B3, 4
• C2, 2
• D2, 3
• E3, 3

Q25:

Find .

• A
• B
• C4
• D
• E