The question is asking whether the statement: "The set of complex numbers is the set of all numbers of the form [tex]\( a + bi \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are real numbers and [tex]\( i = \sqrt{-1} \)[/tex]" is true.
To determine if this statement is true, we need to understand the definition of a complex number.
A complex number is a number in the form [tex]\( a + bi \)[/tex], where:
- [tex]\( a \)[/tex] is the real part.
- [tex]\( b \)[/tex] is the imaginary part.
- [tex]\( i \)[/tex] is the imaginary unit, defined as [tex]\( \sqrt{-1} \)[/tex].
Given this definition, the statement can be broken down as follows:
- [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are real numbers. This means both parts of the complex number do not include any imaginary units by themselves.
- [tex]\( i \)[/tex] is the imaginary unit, [tex]\( \sqrt{-1} \)[/tex]. This is a standard definition in complex number theory.
Since the statement aligns perfectly with the definition of a complex number, it accurately describes the set of complex numbers.
Hence, the statement is:
A. True
