To simplify the given expression by graphing, we will follow two steps.
Graph 6+5i and - 2-3i on the same complex plane and connect each point with the origin.
Complete the parallelogram that has the two segments from Step 1 as two of its sides and plot a point where the two new sides meet.
The point where the two new sides meet is the sum of the complex numbers.
Step 1
In a complex plane, the horizontal axis represents the real part and the vertical axis represents the imaginary part of a complex number. With this in mind, let's graph 6+5i and - 2-3i.
Step 2
Let's now complete the parallelogram. To do so, we must recall that the opposite sides of a parallelogram are parallel and congruent. We will also identify the intersection of the two additional sides.
The intersection of the new sides occurs at the point 4+2i. Therefore, the solution of (6+5i)+(- 2-3i) is 4+2i.
