Write three examples of complex numbers. Make one example be just an integer, the next example a purely imaginary number, and the last example have both an a and b that is not zero. Then, re-write each of your complex numbers in a + bi form and identify the real and imaginary part.

Answer 1

Sure! Here are three examples of complex numbers:

1. Example of an integer:

   • Complex Number: \( 5 \)
   • In \( a + bi \) form: \( 5 + 0i \)
   • Real part: \( 5 \)
   • Imaginary part: \( 0 \)

2. Example of a purely imaginary number:

   • Complex Number: \( -3i \)
   • In \( a + bi \) form: \( 0 + (-3)i \)
   • Real part: \( 0 \)
   • Imaginary part: \( -3 \)

3. Example of a complex number with both real and imaginary parts non-zero:

   • Complex Number: \( 4 + 2i \)
   • In \( a + bi \) form: \( 4 + 2i \)
   • Real part: \( 4 \)
   • Imaginary part: \( 2 \)

To summarize:

1. \( 5 \) is \( 5 + 0i \) with \( \text{Real part} = 5, \text{Imaginary part} = 0 \).
2. \( -3i \) is \( 0 - 3i \) with \( \text{Real part} = 0, \text{Imaginary part} = -3 \).
3. \( 4 + 2i \) has \( \text{Real part} = 4, \text{Imaginary part} = 2 \).