The addition operation is defined as follows, given two complex numbers $z_1$ and $z_2$:

$z_1 + z_2 = (a_1 + b_1 i )+(a_2 + b_2 i) = (a_1 + a_2)+(b_1 + b_2) i$

Notice that the only real parts can be added to real parts and only complex parts can be added to complex parts. The subtraction operation is defined similarly.

$z_1 - z_2 = (a_1 + b_1 i)-(a_2 + b_2 i) = (a_1-a_2)+(b_1-b_2)i$

Examples :

$(1+i) + (2+3i) = 3+4i$

$(5+i)-(3+5i) = 2-4i$

Filed under : Crash Courses, Mathematics

Sources used

• Complex Variables and Applications by James Ward Brown and Ruel V. Churchill
• Complex Analysis by Serge Lang
• Chaos and Fractals by Pietgen, Jurgens and Saupe
• Fundamentals of Electric Circuits by Charles K. Alexander and Matthe N.O. Sadiku