Real numbers and purely imaginary numbers are both special cases of complex numbers, which are defined as numbers that can be expressed in the form \( a + bi \), where \( a \) is the real part and \( b \) is the coefficient of the imaginary unit \( i \). For instance, a real number like \( 5 \) can be written as \( 5 + 0i \) (where the imaginary part is zero), and a purely imaginary number like \( 3i \) can be expressed as \( 0 + 3i \) (where the real part is zero). To identify the real and imaginary parts of a complex number, simply separate the number into its constituent parts, identifying the value before the \( i \) as the real part and the coefficient of \( i \) as the imaginary part.
In 3 sentences, describe why real numbers and purely imaginary numbers are also complex numbers composed of real and imaginary parts. Also, describe how to identify the real part versus the imaginary part of a complex number.
3 answers
Answer like an 11th grader
Real numbers and purely imaginary numbers are actually types of complex numbers because they can fit into the format \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part. For example, the number \( 4 \) is a real number that can be written as \( 4 + 0i \), while \( 5i \) is a purely imaginary number that can be written as \( 0 + 5i \). To figure out the real and imaginary parts of a complex number, just look for the part without \( i \) (that’s the real part) and the number in front of \( i \) (that’s the imaginary part).