# How do you add (-3+i) + (4+6i)?

Mar 29, 2018

$1 + 7 i$. See explanation below

#### Explanation:

The addition in $\mathbb{C}$ is defined by

$\left(a + b i\right) + \left(c + \mathrm{di}\right) = \left(a + c\right) + \left(b + d\right) i$. The two complex numbers addition consists in adding real parts and imaginary parts separately.

In our case

$\left(- 3 + i\right) + \left(4 + 6 i\right) = \left(- 3 + 4\right) + \left(1 + 6\right) i$ because the imaginary part of first complex number is 1. Then we have:

$\left(- 3 + 4\right) + \left(1 + 6\right) i = 1 + 7 i$