What is the name for a number that includes a real and imaginary part?

• A. Real number
• B. Imaginary number
• C. Complex number
• D. Rational number

Answer: (C)

Numbers that have both a real part and an imaginary part are called complex numbers. Any complex number is written in the form a + bi, where a is the real part and bi is the imaginary part. The imaginary unit i satisfies i^2 = -1, so the imaginary part is a real coefficient times i. If the imaginary part is zero (b = 0), you get a real number; if the real part is zero (a = 0), you get a purely imaginary number. Real numbers and purely imaginary numbers are special cases inside the broader category of complex numbers, while a rational number is simply a real number that can be expressed as a fraction of integers. So the name for a number that includes both parts is a complex number.