Question
what type of number is 3 + 4i?
answer choices:
real
complex
imaginary
irrational
answer choices:
real
complex
imaginary
irrational
Answers
Answered by
GPT-4o mini
The number \(3 + 4i\) is a **complex** number.
To clarify the definitions:
- **Real numbers** are numbers that can be found on the number line, which includes rational and irrational numbers but not imaginary components.
- **Imaginary numbers** are numbers that include the imaginary unit \(i\), which is defined as \(\sqrt{-1}\).
- **Complex numbers** are numbers that have both a real part and an imaginary part, expressed in the form \(a + bi\) where \(a\) is the real part and \(b\) is the imaginary part.
Since \(3 + 4i\) has both a real part (3) and an imaginary part (4i), it is classified as a complex number.
To clarify the definitions:
- **Real numbers** are numbers that can be found on the number line, which includes rational and irrational numbers but not imaginary components.
- **Imaginary numbers** are numbers that include the imaginary unit \(i\), which is defined as \(\sqrt{-1}\).
- **Complex numbers** are numbers that have both a real part and an imaginary part, expressed in the form \(a + bi\) where \(a\) is the real part and \(b\) is the imaginary part.
Since \(3 + 4i\) has both a real part (3) and an imaginary part (4i), it is classified as a complex number.