How do you simplify (6+4i)-(-5+i)?

Dec 25, 2015

Explanation:

Example 1: Add $a + i b$ and $c + i d$

$a + i b + c + i d = a + c + i b + i d$
$= \left(a + c\right) + i \left(b + d\right)$

When we add complex numbers we add the real parts together and imaginary part together.

Example 2: $\left(a + i b\right) - \left(c + i d\right)$

$\left(a + i b\right) - \left(c + i d\right)$
$= a + i b - c - i d$ distribute the negative
$= a - c + i b - i d$
$= \left(a - c\right) + i \left(b - d\right)$

When we subtract the complex numbers, find the difference of real and difference of imaginary part

Now let us come to our problem

$\left(6 + 4 i\right) - \left(- 5 + i\right)$
$= 6 + 4 i + 5 - i$
$= 6 + 5 + 4 i - i$
$= 11 + 3 i$ Answer .