What number must we add to 3-5i to get 2+7i ? Here, i^2=-1
We can turn this problem into a subtraction problem: (2+7i) - (3-5i).
Since the order of subtraction/addition problems don't matter (a+b=b+a and a-b=-b+a), we can turn the problem into: (2-3) + (7i - -5i)
Subtracting a negative number is like adding the positive version of it: (2-3) + (7i+5i)
Doing the parts individually, 2-3 = -1 and 7i+5i = 12i.
Finally, we can combine them and our solution is -1 + 12i or 12i - 1.
I hope this helped :)