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