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# Compute the modulus and principal argument of given complex numbers

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

1. .
2. .
3. .
4. .
5. .
6. .
7. .
8. .
9. .
10. .

1. 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 2. First, the modulus is given by The principal argument satisfies 3. The modulus is given by The principal argument satisfies 4. The modulus is given by The principal argument satisfies 5. The modulus is given by The principal argument satisfies 6. The modulus is given by The principal argument satisfies 7. First, we write in the form , Therefore, the modulus is The principal argument satisfies 8. First, we rewrite in the form , Therefore, the modulus is The principal argument satisfies 9. First, we rewrite in the form , Therefore, the modulus is The principal argument satisfies 10. First, we rewrite in the form , The modulus is The principal argument satisfies 