# Worksheet: Matrix Representation of Complex Numbers

In this worksheet, we will practice representing a complex number as a linear transformation matrix and using this to determine the product of two complex numbers.

Q1:

Suppose we take the matrix to represent the complex number and the matrix to represent the complex number .

What is the product ?

• A
• B
• C
• D
• E

What does it represent?

• AThis is the matrix representing which is the product
• BThis is the matrix representing which is the product
• CThis is the matrix representing which is the product .
• DThis is the matrix representing which is the product .
• EThis is the matrix representing which is the product .

Q2:

Describe the geometric transformation that occurs when numbers in the complex plane are mapped to their sum with .

• Aa translation by
• Ba translation by
• Ca translation by
• Da translation by
• Ea translation by

Q3:

Let be the matrix representation of the complex number .

Express the matrix representation of in terms of .

• A
• B
• C
• D

What does correspond to in relation to ?

• AThe determinant, , corresponds to .
• BThe determinant, , corresponds to .
• CThe determinant, , corresponds to .
• DThe determinant, , corresponds to .

What does correspond to in terms of ?

• AThe matrix inverse, , corresponds to the complex number .
• BThe matrix inverse, , corresponds to the complex number .
• CThe matrix inverse, , corresponds to the complex number .
• DThe matrix inverse, , corresponds to the complex number .

Q4:

Suppose we take the matrix to represent the complex number and the matrix to represent the complex number .

What is the sum ?

• A
• B
• C
• D
• E

What does this represent in terms of the complex numbers and ?

• A
• B
• C

Q5:

Let be the matrix representation of the complex number and be the matrix representation of . Determine the matrix representation of .

• A
• B
• C
• D
• E

Q6:

Let the complex numbers , , and be represented by the matrices , , and . Rewrite the following complex calculation as a matrix calculation:

• A
• B
• C
• D
• E

Q7:

Let be the matrix representation of the complex number . What is the corresponding complex number identity for the matrix identity where is the cofactor matrix of ?

• A
• B
• C
• D
• E