Answer
The addition of a complex number is such that we add the real part with the real part and add the imaginary part with the imaginary part.
Work Step by Step
Consider the two complex numbers, $\left( a+bi \right)$and $\left( c+di \right)$
A complex number contains a real part and an imaginary part.
The real part is the term which is independent from the imaginary unit $i$ and the imaginary part is the term which is the multiple of $i$.
If a complex number is in the standard form$\left( a+bi \right)$ then the real part is $a$ and the imaginary part is $b$. In the complex number $\left( c+di \right)$, the real part is $c$ and the imaginary part is $d$.
To add the two complex numbers, add the real part with a real part and add the imaginary part with an imaginary part.
$\left( a+bi \right)+\left( c+di \right)=\left( a+c \right)+\left( b+d \right)i$s
Procedure to add the two complex numbers.
1. Identify the real part and the imaginary part.
2. Add the real part with the real part.
3. Add the imaginary part with the imaginary part.
4. Write the answer in standard form.
For example,
Consider the two complex numbers, $\left( 1+2i \right)$ and $\left( 3+4i \right)$
Identify the real part and imaginary part.
The real parts are $1$, $3$ and the imaginary parts are $2$, $4$.
Add the real part $1$ with the real part $3$ and add the imaginary part $2$ with the imaginary part $4$.
$\begin{align}
& \left( 1+2i \right)+\left( 3+4i \right)=1+2i+3+4i \\
& =\left( 1+3 \right)+\left( 2+4 \right)i
\end{align}$
Write the answer in standard form.
$\left( 1+2i \right)+\left( 3+4i \right)=4+6i$
Therefore, the addition of two complex numbers is such that we add the real part with the real part and add the imaginary part with the imaginary part.
