## Addition of Two Complex Numbers

If we have two complex numbers and then we can add them together

Graphically complex addition is the same as vector addition. We construct a parallelogram and find its diagonal. Diagram below illustrates complex addition. Geometrically adding a complex number with a complex number will translate to the right with amount of and shifted upward with amount of .

### Complex Number Calculator

First number: real part imaginary part Second number: real part imaginary part Operation

### Properties of Complex Addition

• Zero complex number is the identity element of complex addition because is the identity element of complex addition because
• Commutative
• Associative
• Triangular Inequality . Point O with A and B form a triangle. One side of the triangle cannot exceed the sum of the other two sides. The modulus of the sum of any complex numbers is not greater than the sum of their moduli. . Point O with A and B form a triangle. One side of the triangle cannot exceed the sum of the other two sides. The modulus of the sum of any complex numbers is not greater than the sum of their moduli.