Math Snap

STEP 1

1. Complex numbers are of the form $a + bi$, where $a$ is the real part and $b$ is the imaginary part.
2. To find the sum of complex numbers, we add their real parts and their imaginary parts separately.

STEP 2

1. Identify the real and imaginary parts of each complex number.
2. Add the real parts together.
3. Add the imaginary parts together.
4. Write the sum in the form $a + bi$.
5. Graph the complex numbers and their resultant.

STEP 3

Identify the real and imaginary parts of each complex number. For the complex number $5 - 6i$, the real part is $5$ and the imaginary part is $-6$. For the complex number $-2 + 4i$, the real part is $-2$ and the imaginary part is $4$.

STEP 4

Add the real parts of the complex numbers:
$$5 + (-2) = 3$$

STEP 5

Add the imaginary parts of the complex numbers:
$$-6 + 4 = -2$$

STEP 6

Combine the results from Step 2 and Step 3 to write the sum in the form $a + bi$:
$$3 - 2i$$

Graph the complex numbers and their resultant:
- Plot the point $(5, -6)$ for the complex number $5 - 6i$.
- Plot the point $(-2, 4)$ for the complex number $-2 + 4i$.
- Plot the point $(3, -2)$ for the resultant complex number $3 - 2i$.
- Draw vectors from the origin to each of these points to represent the complex numbers.
The sum of the pair of complex numbers is:
$$\boxed{3 - 2i}$$