In Exercises 1 − 14 , decide whether each of the given sets is a group with respect to the indicated operation. If it is not a group, state a condition in Definition 3.1 that fails to hold. The set of all complex numbers x that have absolute value 1 , with operation multiplication. Recall that the absolute value of a complex number x written in the form x = a + b i , with a and b real, is given by | x | = | a + b i | = a 2 + b 2 .
In Exercises 1 − 14 , decide whether each of the given sets is a group with respect to the indicated operation. If it is not a group, state a condition in Definition 3.1 that fails to hold. The set of all complex numbers x that have absolute value 1 , with operation multiplication. Recall that the absolute value of a complex number x written in the form x = a + b i , with a and b real, is given by | x | = | a + b i | = a 2 + b 2 .
In Exercises
1
−
14
, decide whether each of the given sets is a group with respect to the indicated operation. If it is not a group, state a condition in Definition
3.1
that fails to hold.
The set of all complex numbers
x
that have absolute value
1
, with operation multiplication. Recall that the absolute value of a complex number
x
written in the form
x
=
a
+
b
i
, with
a
and
b
real, is given by
|
x
|
=
|
a
+
b
i
|
=
a
2
+
b
2
.
Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.