Every imaginary number is also a complex number?

Question

How is it possible that every imaginary number (multiple of i ) is also a complex number?

Answer 1

The standard definition of a complex number is any number that can be written as: $a+b\,i$ where $a,b\in\Bbb R$ and $i=\sqrt{-1}$. So even an imaginary number, that is a number of the form $b\,i$, is a complex number since it can be written as: $0+b\,i$.

Answer 2

Any real multiple of $ i $, say $ ai $, is also a complex number $0+ai $. Complex number is a number of the form $ a+bi$, where $ a, b\in \mathbb {R} $. Zero is obviously a real number, so everything works out nicely.

Answer 3

First of all, lets see the definition of a complex number:

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit,

For an imaginaty number it is: 0+bi

Note that 0 is a real number, so it didn't break the rule.

Similarly any real number is: a+0i which is a complex number too.