Question

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

Answer 1

Answer:

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

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 $9+i\,7$.