Complex number with real part as 0

Question

it is kinda of awkward, but is

Equation:

0+3i=0?

Or it simply means that it is imaginary number?

Answer 1

$0 + 3i$ and $0$ are two distinct complex numbers.

• $0 + 3i = 3i$ is an "imaginary number", which means it is on the $y$-axis of the complex plane.

• $0$ is at the origin of the complex plane.

Answer 2

Every real number is a complex number, and every imaginary number is also a complex number. In this sense, $3i$ can be both viewed as an imaginary number (Since $\Re(3i)=0$) and as a complex number.

Answer 3

Examples of real numbers are $1,2,3,\ldots$

Examples of imaginary numbers are $\mathrm{i},2\mathrm{i},3\mathrm{i},\ldots$

Complex numbers are a mixture of the two, e.g. $1+2\mathrm{i}$ or $7-3\mathrm{i}$, etc.

In general, a complex number looks like $x+y\mathrm{i}$ where $x$ and $y$ are both real numbers.

The numbers $x$ and $y$ are called the real and imaginary parts respectively.

The complex number zero has zero real part and zero imaginary part: $0+0\mathrm{i}$.

Your example $0+3\mathrm{i}$ is not zero because it has a non-zero imginary part.

If $w=a+\mathrm{i}b$ and $z=c+\mathrm{i}d$ are two complex numbers then $w=z$ if, and only if, $a=c$ and $b=d$.