# 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