Question

Identify which of the following are imaginary numbers: i^2, 1+i, 42i, πi, 2.

Answer 1

Imaginary numbers are defined as a real number multiplied by the imaginary unit i. In the list provided, 42i and πi are purely imaginary, while 1+i is complex but not purely imaginary, and 2 is a real number.

Step-by-step explanation:

In the field of mathematics, specifically complex numbers, imaginary numbers are a subset of complex numbers where the number can be written as a real number multiplied by the imaginary unit i, which is defined as the square root of -1. Examples of imaginary numbers include i2, which is -1 and is not imaginary, while 42i and πi are purely imaginary. The number 1+i is a complex number because it has both a real part (1) and an imaginary part (i), but it is not purely imaginary. Lastly, the number 2 is a real number and not an imaginary or complex number.