Question

How do you find the real and imaginary part $\pi +i$?

Answer 1

Here we will compare the given expression with the general form of the complex number given as $z=x+iy$, where x is called the real part of z denoted as Re (z) and y is called the imaginary part if z denoted as Im (z). $i$ is the symbol of imaginary number $\sqrt{-1}$.

Complete step by step solution:
Here we have been provided with the expression $\pi +i$ and we are asked to determine its real and imaginary part. But first we need to know what does the symbol $i$ signify?
Now, here the expression provided to us is a complex number. A complex number is a combination of a real number and an imaginary number. In general all the numbers are complex numbers. The general form of a complex number (z) is represented as: $z=x+iy$. Here, x is called the real part of z denoted as Re (z) and y is called the imaginary part if z denoted as Im (z). $i$ is the symbol of imaginary number $\sqrt{-1}$ which is read as ‘iota’.
Now, let us compare the given expression with $x+iy$. So, we have,
$\Rightarrow \pi +i=x+iy$
On comparing we get,
$\Rightarrow x=\pi$ and $y=1$.

Hence, the real part of z is Re (z) = $\pi$ while the imaginary part is Im (z) = 1.

Note: Remember that all the numbers are actually a subset of complex numbers. Whether we have a real number or imaginary number it will always be a complex number in a certain perspective according to the definition. If we have Re (z) = 0 then the complex number is called purely imaginary while if we have Im (z) = 0 then the complex number is called purely real. We cannot use a real plane to plot complex numbers but there is a different plane known as the argand plane for the representation of the same.