For each of the following complex numbers, compute the modulus and principal argument.

- .
- .
- .
- .
- .
- .
- .
- .
- .
- .

- First, the modulus is given by
The principal argument is the unique such that

In this case we have , and so the principal argument satisfies

- First, the modulus is given by
The principal argument satisfies

- The modulus is given by
The principal argument satisfies

- The modulus is given by
The principal argument satisfies

- The modulus is given by
The principal argument satisfies

- The modulus is given by
The principal argument satisfies

- First, we write in the form ,
Therefore, the modulus is

The principal argument satisfies

- First, we rewrite in the form ,
Therefore, the modulus is

The principal argument satisfies

- First, we rewrite in the form ,
Therefore, the modulus is

The principal argument satisfies

- First, we rewrite in the form ,
The modulus is

The principal argument satisfies