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
Properties of Complex Addition
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Zero complex number
is the identity element of complex addition because
is the identity element of complex addition because
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Commutative
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Associative
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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.
See Also : Complex Subtraction , Complex Multiplication , Complex Arithmetic , Vector Addition
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