Answered

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

Sagot :

xero099

Answer:

The sum of the complex numbers is [tex]9+i\,7[/tex].

Explanation:

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

1) [tex]u = 6 + i\,2[/tex], [tex]v = 3 + i\,5[/tex] Given.

2) [tex]u+v = (6+i\,2)+(3+i\,5)[/tex] Definition of addition.

3) [tex]u+v = (6+3) + (2\,i + 5\,i)[/tex] Commutative and associative properties.

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

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

The sum of the complex numbers is [tex]9+i\,7[/tex].

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