Question

What is the sum of the complex numbers 6+2i and 3+5i, where i=sqrt(-1)

Answer 1

The sum of the complex numbers is
`9+i\,7`.

Step-by-step explanation:

Let be
`u = 6 + i\,2` and
`v = 3 + i\,5`, the sum of the complex number can be found by algebraic means. That is:

1)
`u = 6 + i\,2`,
`v = 3 + i\,5` Given.

2)
`u+v = (6+i\,2)+(3+i\,5)` Definition of addition.

3)
`u+v = (6+3) + (2\,i + 5\,i)` Commutative and associative properties.

4)
`u+v = 9 + (2+5)\,i` Definition of addition/Distributive property.

5)
`u + v = 9 + i\,7` Definition of addition/Commutative property/Result.

The sum of the complex numbers is
`9+i\,7`.