Complex numbers are defined as numbers that can be expressed in the form \( a + bi \), where \( a \) represents the real part and \( b \) represents the imaginary part, with \( i \) being the imaginary unit (the square root of -1). Real numbers are a specific case of complex numbers where the imaginary part is zero (e.g., \( a + 0i \)), while purely imaginary numbers have a real part equal to zero (e.g., \( 0 + bi \)). To identify the real part of a complex number, you look at the coefficient of the term without \( i \), while the coefficient of the term with \( i \) represents the imaginary part. For example, in the complex number \( 3 + 4i \), the real part is \( 3 \) and the imaginary part is \( 4 \).
Question
In 3–5 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
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