Given two complex numbers:
\(z_2=c+di, z_1=a+bi \)
their sum is:
\(z_1+z_2=(a+bi)+(c+di)=(a+c)+(b+d)i \)
The real part of the sum equals the sum of the real parts of the two numbers.
The imaginary part of the sum equals the sum of the imaginary parts of the two numbers.
Below is an interactive GeoGebra illustration of complex number addition.
The imaginary axis is the vertical axis; the real axis is the horizontal axis.
We have 2 numbers: \(z_1=5-i\) and \(z_2=1+4i\)
Click the checkbox to see their sum and display the parallelogram.