Answer
The sum of is $-3i$.
See Graph I, the resultant $-3i$ is in RED.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/9b1472fc-a2fc-4998-a86a-6597384337bc/result_image/1510078588.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015448Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=2435586f731591a318b115d6d635a44170541f2e08c0a3bdfdba41833a98a834)
Work Step by Step
The sum of $5 - 6i$ and $-5 + 3i$ is $-3i$.
Refer to Graph I, the complex number, $5 - 6i$ and $-5 + 3i$ are in BLUE, while the resultant $-3i$ is in RED.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/9b1472fc-a2fc-4998-a86a-6597384337bc/steps_image/small_1510078588.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015448Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=5b41a2809b9e6dbae680b35b39de2b41aff9cc68043747a2dbce8847f8777d88)