# Worksheet: Introduction to Complex Numbers

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:

Is the following statement true or false: Any complex number is also a real number.

• Afalse
• Btrue

Q2:

If , what is ?

Q3:

If , what is ?

Q4:

Which of the following statements will be true of two equal complex numbers?

• ATheir real parts will not be equal and their imaginary parts will not be equal.
• BTheir real parts will be equal and their imaginary parts will not be equal.
• CTheir real parts will be equal and their imaginary parts will be equal.
• DTheir real parts will not be equal and their imaginary parts will be equal.

Q5:

Is the following statement true or false: Any imaginary number is also a complex number.

• Afalse
• Btrue

Q6:

What type of number is ?

• Areal
• Bcomplex
• Cpurely imaginary

Q7:

What is the real part of the complex number ?

Q8:

What is the imaginary part of the complex number ?

Q9:

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

Q10:

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

Q11:

If , which of the following statements is correct?

• A,
• B,
• C,
• D,
• E,

Q12:

• A
• B
• C
• D
• E

Q13:

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

• ATrue
• BFalse

Q14:

Factor over the complex numbers.

• A
• B
• C
• D
• E

Q15:

Express in terms of .

• A
• B
• C
• D
• E

Q16:

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