Addition and Subtraction

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

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  1. What are Complex Numbers
  2. Addition and Subtraction
  3. Multiplication
  4. Modulus and the Complex Plane
  5. Division
  6. Phasor
  7. Applications of Complex Numbers

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

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